Crossed products of Hilbert C*-bimodules by countable discrete groups

Abstract

We introduce a notion of crossed products of Hilbert C ∗ {}^{*} -bimodules by countable discrete groups and mainly study the case of finite groups following Jones index theory. We give a sufficient condition such that the crossed product bimodule is irreducible. We have a bimodule version of Takesaki-Takai duality. We show the categorical structures when the action is properly outer, and give some example of this construction concerning the orbifold constructions.