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What is the equivariant cohomology of a group acting on itself by conjugation?

Let $G$ be a compact Lie group. Where can one read about the equivariant cohomology $H_G^*(G)$, where $G$ acts on itself by the adjoint action? A study of a concrete example (like SU(2)) would already be useful for me. Thanks!

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This question has already been asked (and answered) here What is the equivariant cohomology of a group acting on itself by conjugation?

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