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Imprimitivity theorems for weakly proper actions of locally compact groups

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, reduced, or exotic crossed products and appropriate universal, reduced, or exotic fixed-point algebras, respectively. In particular, we obtain an exotic version of Green's imprimitivity theorem and a very general version of the symmetric imprimitivity theorem 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.