  We analzye Rieffel's construction of generalized fixed point algebras in the
setting of group actions on Hilbert modules. Let G be a locally compact group
acting on a C*-algebra B. We construct a Hilbert module F over the reduced
crossed product of G and B, using a pair (E, R), where E is an equivariant
Hilbert module over B and R is a dense subspace of E with certain properties.
The generalized fixed point algebra is the C*-algebra of compact operators on
F. Any Hilbert module over the reduced crossed product arises by this
construction for a pair (E, R) that is unique up to isomorphism.
  A necessary condition for the existence of R is that E be square-integrable.
The consideration of square-integrable representations of Abelian groups on
Hilbert space shows that this condition is not sufficient and that different
choices for R may yield different generalized fixed point algebras.
  If B is proper in Kasparov's sense, there is a unique R with the required
properties. Thus the generalized fixed point algebra only depends on E.

Operator Algebras