Imprimitivity for $C^*$-Coactions of Non-Amenable Groups

Abstract

We give a condition on a full coaction $(A,G,\delta)$ of a (possibly) nonamenable group $G$ and a closed normal subgroup $N$ of $G$ which ensures that Mansfield imprimitivity works; i.e. that $A\times_{\delta{\vert}} G/N$ is Morita equivalent to $A\times_\delta G\times_{\deltahat,r} N$. This condition obtains if $N$ is amenable or $\delta$ is normal. It is preserved under Morita equivalence, inflation of coactions, the stabilization trick of Echterhoff and Raeburn, and on passing to twisted coactions.