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If New York is a city of dreams, Anna Sorokin had plenty of them.

Ms. Sorokin, a Russian immigrant from a middle-class family, longed to be a member of the upper echelon of Manhattan society. She elbowed her way into the city’s bustling social scene and tried to raise money to open a members-only arts club on Park Avenue South.

To friends and those wanting to do business with her, there was no reason to believe she was not the person she said she was — a wealthy German heiress with a taste for the high life.

For years, she had played the part, and looked it, too. She wore the latest designer clothes — Gucci and Yves Saint Laurent — and moved from one boutique hotel to the next. She doled out $100 tips, treated friends to expensive meals and chartered a private plane to Omaha for the Berkshire Hathaway Conference.