Imprimitivity for $C^{\ast }$-Coactions of Non-Amenable Groups

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 $A{\times }_{\delta \mathrm{\mid }}G\mathrm{/}N$ is Morita equivalent to $A{\times }_{\delta }G{\times }_{\text{deltahat},r}N$. 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.