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.
