A new equivariant cohomology ring

Abstract

In this paper, motivated by Chen–Ruan’s stringy orbifold theory on almost complex orbifolds, we construct a new equivariant cohomology ring $${\mathscr {H}}^*_G(X)$$ for an equivariant almost complex pair (X, G), where X is a compact connected almost complex manifold, G is a connected compact Lie group which acts on X and preserves the almost complex structure.