  We generalize the results of a previous paper of ours to compact Lie groups.
Using a recently developed ordinary equivariant homology and cohomology, we
define equivariant Poincare complexes with the properties that (1) every
compact G-manifold is an equivariant Poincare complex, (2) every finite
equivariant Poincare complex (with some mild additional hypotheses) has an
equivariant spherical Spivak normal fibration, and (3) the Pi-Pi Theorem holds
for equivariant Poincare pairs under suitable gap hypotheses. The nice behavior
of the ordinary equivariant homology and cohomology theories allows us to
follow Wall's original line of argument closely.
