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Let $X$ be a topological space with a continuous action by a finite group $G$. Hopefully under some assumptions on $X$ one can identify the rational cohomology of $X/G$ with the $G$-invariants of the rational cohomology of $X$. Can anyone explain this or provide a reference?

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For nice enough $X$ you have $H^i(X/G;\mathbb{Q}) = H^i_G(X;\mathbb{Q})$, by a standard spectral sequence argument in group cohomology (see Ken Brown's text on the subject, section VII.7)... For general degrees I don't think this relates to the G-invariants. – Chris Gerig Jul 27 '12 at 21:30

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