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

Let $G$ be a discrete group acting on a von Neumann algebra $M$ by properly\nouter $*$-automorphisms. In this paper we study the containment $M \\subseteq\nM\\rtimes_\\alpha G$ of $M$ inside the crossed product. We characterize the\nintermediate von Neumann algebras, extending earlier work of other authors in\nthe factor case. We also determine the $M$-bimodules that are closed in the\nBures topology and which coincide with the $w^*$-closed ones under a mild\nhypothesis on $G$. We use these results to obtain a general version of Mercer's\ntheorem concerning the extension of certain isometric $w^*$-continuous maps on\n$M$-bimodules to $*$-automorphisms of the containing von Neumann algebras.\n