See Equivariant Ordinary Homology and Cohomology by Steve Costenoble and I, now in arxiv.org, for a comprehensive theory of Poincare duality in ordinary equivariant homology and cohomology (as opposed to Borel homology/cohomology) for compact Lie group actions.

See the paper Equivariant Ordinary Homology and Cohomology by Steve Costenoble and myself for a comprehensive theory of Poincare duality in ordinary equivariant homology and cohomology (as opposed to Borel homology/cohomology) for compact Lie group actions.