A group led by Tishman Speyer Properties has decided to give up the sprawling Peter Cooper Village and Stuyvesant Town apartment complex in Manhattan to its creditors in the collapse of one of the most high-profile deals of the real-estate boom.

The decision comes after the venture between Tishman and BlackRock Inc. defaulted on the $4.4 billion debt used to help finance the deal. The venture acquired the 56-building, 11,000-unit property for $5.4 billion in 2006—the most ever paid for a single residential property in the...