Representations of group algebras in spaces of completely bounded maps

Let G be a locally compact group, pi : G -> U(H) be a strongly continuous unitary representation, and CBsigma (B(H)) the space of normal completely bounded maps on B(H). We study the range of the map Gamma(pi) : M(G) -> CBsigma (B(H)), Gamma(pi) (mu) = integral(G) pi(s) circle times pi (s)* d mu(s), where we identify CBsigma(B(H)) with the extended Haagerup tensor product B(H) circle times(eh) B(H). We use the fact that the C*-algebra generated by integrating pi to L-1(G) is unital exactly when pi is norm continuous, to show that Gamma(pi)(L-1(G) subset of B(H)circle times(h) B(H) exactly when pi is norm continuous. For the case that G is abelian, we study F-pi(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.