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

Abstract

AbstractWe prove theK-theoretic Farrell–Jones conjecture for groups with the Haagerup approximation property and coefficient rings andC^{*}-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 groupG, to show that the algebraic and theC^{*}-crossed product ofGwith a stable separableG-C^{*}-algebra have the sameK-theory.