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.