Compact operators and algebraic K-theory for groups which act properly and isometrically on Hilbert space.

We prove the K-theoretic Farrell-Jones conjecture for groups with the Haagerup approximation property and coefficient rings and C*-algebras which are stable with respect to compact operators. We use this and Higson-Kasparov's result that the Baum-Connes conjecture holds for such a group G, to show that the algebraic and the C*-crossed product of G with a stable separable G-C*-algebra have the same K-theory. [ABSTRACT FROM AUTHOR]