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Let $G$ be a discrete group acting on a von Neumann algebra $M$ by properlyouter $*$-automorphisms. In this paper we study the containment $M \subseteqM\rtimes_\alpha G$ of $M$ inside the crossed product. We characterize theintermediate von Neumann algebras, extending earlier work of other authors inthe factor case. We also determine the $M$-bimodules that are closed in theBures topology and which coincide with the $w^*$-closed ones under a mildhypothesis on $G$. We use these results to obtain a general version of Mercer'stheorem concerning the extension of certain isometric $w^*$-continuous maps on$M$-bimodules to $*$-automorphisms of the containing von Neumann algebras.

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