Let G and H be two locally
compact groups acting on a C∗-algebra A by commuting actions λ and σ. We
construct an action on A×λG out of σ and a unitary cocycle u. For A commutative,
and free and proper actions λ and σ, we show that if the roles of λ and σ are
reversed, and u is replaced by u∗, then the corresponding generalized fixed-point
algebras, in the sense of Rieffel, are strong-Morita equivalent. This fact turns out to
be a generalization of Green’s result on the strong-Morita equivalence of the
algebras C0(M∕H) ×λG and C0(M∕G) ×σH. Finally, we use the Morita
equivalence mentioned above to compute the K-theory of quantum Heisenberg
manifolds.
