Selling perfume is about dreams. For fantasies of sex and glamour, spritz Tom Ford. For understated chic, use Armani. So what are we to make of the small bottle of perfume in an aquamarine leather box, soberly displayed on the shelves of Saks Fifth Avenue in Dubai? There’s a message in this bottle, and the clue is in its name, written in lush Arabic script: Mukhalat al-Sheika Lubna, which translates roughly as "Mix of Sheika Lubna." The name Sheika Lubna may not mean much in the West, but in the United Arab Emirates, it's synonymous with big money. Sheika Lubna al-Qasimi is a fast-talking, media-friendly 50-year-old princess who, as foreign trade minister of the U.A.E., is leading the most aggressive economic and social revolution in the region. She has helped turn the emirates, awash in oil money, into an Arab version of Las Vegas, all upscale resorts and over-the-top attractions. And she has helped direct some of its cash toward the West, through investments in Western companies, many of them struggling because of the sagging U.S. economy. While Sheika Lubna may not control the U.A.E.'s purse strings—investments are determined by the managers of the Dubai and Abu Dhabi sovereign wealth funds—she is the face of the emirates for the West, the most prominent emissary other than Sheik Mohammed bin Rashid al-Maktoum, the U.A.E.'s prime minister and ruler of Dubai. Thanks largely to Sheika Lubna, the U.A.E. has become the biggest recipient of foreign investment in the Middle East. (View an interactive feature showing Mideast investments in U.S. companies.)

But with economic expansion has come friction. In 2006, DP World, a business backed by the government of Dubai, was forced to sell the U.S. port-management operations it had acquired through the purchase of a British company. A political firestorm had erupted in the U.S. over fears that a Middle Eastern firm’s involvement in running port facilities could jeopardize national security. More recently, there has been dark talk that the U.A.E.'s ports are being used by enemies of the U.S., including Iran.

The sheika's role is to deflect criticism while keeping the cash rolling in. She has the right qualifications. She is the first Arab woman to create a multimillion-dollar e-commerce company in a region where women have traditionally played only bit roles in business. She's also the first woman to become the economic minister of an oil-rich nation and the only cabinet minister anywhere to have her own perfume. Think Carly Fiorina meets Condoleezza Rice, with a touch of Oprah Winfrey.

All of Sheika Lubna's firsts make it easy to forget that the U.A.E. is a nation very much in transition. The sheika's job is to represent that shift while at the same time making it look as effortless as possible.

Walking out of the elevator to visit Sheika Lubna's office in downtown Abu Dhabi, I almost bump into her. "You're early," she says, holding out a firm hand. Many Arab women, even thoroughly modern ones, dislike publicly touching men to whom they are not related. Not Sheika Lubna. Over sweet coffee and fruit juice, she makes small talk, showing off photographs of herself with Bill Clinton, Bill Gates, Colin Powell, and Sheik Mohammed of Dubai. She lists her recent and upcoming engagements in Brussels, London, Paris, and Riyadh. She sees it as part of her job to be "an Arab capable of communicating across cultures." She says, "I support both sides. I argue for America in the U.A.E. and for the U.A.E. in America."

Indeed, Sheika Lubna personifies everything that the U.A.E. and much of modern Arabia aspires to be. To outsiders, the U.A.E. is all bling, a desert full of five-star hotels, skyscrapers, ski domes, million-dollar horse races, and mile-long malls where Russians queue to buy Fendi fur coats despite the 100-degree heat. It’s certainly gaudy. But beyond the razzle-dazzle is a steely sociopolitical mission.

The rulers of Abu Dhabi and Dubai—the two largest and most powerful emirates in the loose federation of seven that make up the U.A.E.—are gambling their current and projected oil revenues on the proposition that they can drag themselves into the modern world. They want to use expensive Middle Eastern oil, cheap East Asian labor, upscale Western professionals, and a sprinkle of celebrity glamour to create a pro-­capitalist, moderate Muslim country that is a socioeconomic success story. Who better to sell the desert dream than an Arab woman who was educated in the U.S.? "I'm used as a front, as a face, partly because I bat for both sides and partly because I'm a woman in a Muslim Arab society," Sheika Lubna says. "It is not something you expect. You immediately get the message that it is an open-minded country."

Clearly, she's much more than a face: How else to explain that since the DP World debacle, the worst moment in the emirates' recent economic ascent, the U.A.E.'s investment in the West has nudged up to $50 billion a year without so much as a raised eyebrow? In 2007, private investment houses and sovereign wealth funds in the emirates have bought into financial giants like Citigroup; two private equity houses, Carlyle Group and Apollo Management; Nasdaq; upscale retailer Barneys New York; gaming behemoth MGM Mirage; and property, hotel, and leisure groups. In Europe, Dubai and Abu Dhabi have bought stakes in airplanemaker E.A.D.S., HSBC, Daimler, Standard Chartered Bank, and the Swedish stock exchange.

In return, the West is buying into the U.A.E.  Overseas investment in the emirates reached a peak of $18 billion in 2006, representing more than one-third of all overseas cash coming into the Middle East. In addition, the U.A.E. is the No. 1 destination for U.S. investment in the region. Sheika Lubna, for instance, helped persuade Halliburton, the oil-services company formerly run by Vice President Dick Cheney, to open a second headquarters in Dubai. Daeman Harris, who leads the U.S. Chamber of Commerce in the Middle East, describes Sheika Lubna as a "superstar." He says, "She has a nuanced understanding of Western and, in particular, American culture. She’s the type of person who can walk into a roomful of U.S. businessmen or government officials who couldn’t find the U.A.E. on a map, give a presentation on the economy and its development, and walk out with everyone in the room saying, 'I've got to get on a plane and see this place for myself.' "

Sheika Lubna is one of seven children born into the extended royal family of Sharjah, the emirate just to the north of Dubai. When she was a child, the most that local girls could hope for was to learn Arabic and math and study the Koran. All that was expected of a minor royal was to marry another royal and have children. But her parents—her father ran the airport there, and her mother was a homemaker—encouraged her to think beyond that. She persuaded them to let her go overseas to learn English and study technology. "I decided to become a total geek," she says. She enrolled in a language school in Britain and soon moved on to study physics and math.

Her brothers persuaded her to swap Britain for the U.S. West Coast. "Two of them were already studying in California. They said that if I really wanted to study technology, I should be there." Sheika Lubna enrolled at California State University at Chico. She was a strict Muslim with a plummy English accent, and her American classmates found it hard to place her. "They used to call me Miss ­Shakespeare," she says.

She admired the American work ethic but turned down job offers in California and headed home to the U.A.E. at age 22. Though her parents urged her to get a government job—the acceptable career track for an establishment woman—she refused. Instead, she joined an Indian-owned software-development firm, becoming the first woman on the payroll.

As her profile grew, her experience and connections earned her a post as the first female member of the management team of Dubai Ports Authority, which in the early 1990s was starting to emerge as a global leader in seaport operations. The men, she says, dismissed her as a secretary and used the salty language of the docks to throw her off stride. But she silenced the bigots by coming up with a computerized manifest system that cut the time it took to handle loose cargo from one hour to 10 minutes.

That success helped her win a $5 mil­lion government grant to set up a new company, Tejari.com, to develop government and business-to-business e-commerce. Within three years, it had broken even and become the biggest e-commerce player in the Middle East. In 2004, she became the first woman to serve in the U.A.E. cabinet, as minister of economy and planning, and then, earlier this year, she was named its first-ever minister of foreign trade.

Today, Sheika Lubna splits her time between Abu Dhabi, the U.A.E.'s seat of government, and Dubai, its financial powerhouse. A few days after our meeting in her Abu Dhabi office, I catch up with her on the top floor of Dubai's Emirates Towers, where Sheik Mohammed has his executive office. From that vantage point, I can see through the windows the future she is selling. Straight ahead is the Dubai International Financial Centre, home to the nascent Bourse Dubai, where just about every major Western bank now has an office. To the left rises the Burj Dubai, the world’s tallest building. To the right, through the heat haze, I can make out the bikini-clad tourists swimming in the Persian Gulf and local businesswomen on mobile phones. Looking at the view with me, Sheika Lubna too is astounded. 'This country is only 36 years old," she says. "I think we’ve achieved a great deal in a generation."

True enough. But there's still a ways to go before the U.A.E.—and, at times, the sheika herself—can be considered genuinely modern. The U.A.E. has no meaningful elections or minimum wage, workers have no right to strike, and abuse of female domestic workers is a serious problem. But when a friend in the government calls to say he'll be late for a meeting because he's dealing with a complaint from the U.S.-based Human Rights Watch, the sheika mocks him: "Don’t talk to me about domestic abuse! I am abusing myself as my own maid, moving all the boxes into my new house." It makes her sound like the princess she is.

I ask her what she thinks would happen if a Saudi woman wanted to launch a perfume in the Riyadh branch of Saks. Uncharacteristically, she ducks the question. "What you see is a different pace of development for women. I cannot impose the pace at which we are going on any other country." Call it mix-and-match morality, or diplomacy, or something else, but Sheika Lubna's approach has allowed her to avoid falling afoul of conservative social and religious forces in the region.

Sheika Lubna's success has come at a heavy personal price. When she was 19, she became engaged to her cousin, and a marriage was arranged. But the relationship fizzled. Since then, she has devoted herself to her career, but she regrets never having married. "I like men. I like kids. I always thought, I am going to do this job, build my career, and the marriage will come along in time. But it never did."

Sheika Lubna is split not just between East and West but also between her roles as a socioeconomic radical and a traditional Arab woman. But she says she has made peace with her past and is happy with her lot. If the first woman to break the mold of Middle Eastern business cannot have it all, so be it. "My proudest achievement is that I am a bridge. Women are following my example. I am changing the mind-set of young girls, saying, 'It’s okay. Look, I'm here. I'm on the other side, and you can breeze through.'"

The first lady of the Gulf pauses and smiles. "Not bad for a geek with a perfume."