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Imprimitivity theorems for weakly proper actions of locally compact groups

Siegfried Echterhoff, Buss, Alcides
published 2013-05-22

In a recent paper the authors introduced universal and exotic generalized fixed-point algebras for weakly proper group actions on C*-algebras. Here we extend the notion of weakly proper actions to actions on Hilbert-modules. As a result we obtain several imprimitivity theorems establishing important Morita equivalences between universal and reduced crossed products and appropriate universal and reduced fixed-point algebras. In particular, we recover Green's imprimitivity theorem and obtain a general version of the symmetric imprimitivity theorem for full and reduced crossed products by weakly proper actions of product groups GxH. In addition, we study functorial properties of generalized fixed-point algebras for equivariant categories of C*-algebras based on correspondences.

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