Abstract
We first show the existence of a weight filtration on the equivariant cohomology of real algebraic varieties equipped with the action of a finite group, by applying group cohomology to the dual geometric filtration. We then prove the compatibility of the equivariant weight filtrations and spectral sequences with Kunneth isomorphism, cup and cap products, from the filtered chain level. We finally induce the usual formulae for the equivariant cup and cap products from their analogs on the non-equivariant weight spectral sequences.
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