Strong invariant approximation property for discrete groups

Abstract

Let G be a countable exact discrete group. We show that G has the approximation property if and only if C* u(G, S) G = Cλ(G) ⊗ S for any Hilbert space H and closed subspace S ⊆ H, we have where C* u(G) is the uniform Roe algebra. This answers a question of J. Zacharias.