Intermediate subalgebras and bimodules for general crossed products of von Neumann algebras

Let G be a discrete group acting on a von Neumann algebra M by properly outer *-automorphisms. In this paper, we study the containment M subset of M x(alpha) G of M inside the crossed product. We characterize the intermediate von Neumann algebras, extending earlier work of other authors in the factor case. We also determine the M- bimodules that are closed in the Bures topology and which coincide with the w*-closed ones under a mild hypothesis on G. We use these results to obtain a general version of Mercer's theorem concerning the extension of certain isometric w*-continuous maps on M- bimodules to *-automorphisms of the containing von Neumann algebras.