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 = C ∗ λ (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.