- Let G be a locally compact group, : G u(H) be a strongly continuous unitary representation, and CB (B(H)) the space of normal completely bounded maps on B(H). We study the range of the map : M(G) CB (B(H)), () = G (s) (s)* d(s), where we identify CB (B(H)) with the extended Haagerup tensor product B(H) eh B(H). We use the fact that the C*-algebra generated by integrating to L1(G) is unital exactly when is norm continuous, to show that (L 1(G)) B(H) h B(H) exactly when is norm continuous. For the case that G is abelian, we study - (M(G)) as a subset of the Varopoulos algebra. We also characterize positive definite elements of the Varopoulos algebra in terms of completely positive operators. Indiana University Mathematics Journal .