Green's theorem for crossed products by Hilbert $C^{\ast }$-bimodules

Abstract

Green's theorem gives a Morita equivalence $C_0(G/H,A)⋊G\sim A⋊H$ for a closed subgroup $H$ of a locally compact group $G$ acting on a $C^{\ast }$-algebra $A$. We prove an analogue of Green's theorem in the case $G=\mathbb{Z}$, where the automorphism generating the action is replaced by a Hilbert $C^{\ast }$-bimodule.