  We consider a class of proper actions of locally compact groups on
imprimitivity bimodules over C*-algebras which behave like the proper actions
on C*-algebras introduced by Rieffel in 1988. We prove that every such action
gives rise to a Morita equivalence between a crossed product and a generalized
fixed-point algebra, and in doing so make several innovations which improve the
applicability of Rieffel's theory. We then show how our construction can be
used to obtain canonical tensor-product decompositions of important Morita
equivalences. Our results show, for example, that the different proofs of the
symmetric imprimitivity theorem for actions on induced algebras yield
isomorphic equivalences. A similar analysis of the symmetric imprimitivity
theorem for graph algebras gives new information about the amenability of
actions on graph algebras.
