The fundamental theorem concerning algebraic K-theory of spaces is the parametrized h-cobordism theorem. It says that stable homotopy includes into A-theory as a summand, and the homotopy fiber of this inclusion is the stable space of smooth h-cobordisms. In this talk we show how to prove the equivariant version of this theorem, using the tom Dieck-style splittings that exist on both A-theory and the stable h-cobordism space.