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How would I prove the following: If the normalization of $X$ can be covered by $G$-invariant quasiprojective open subsets, then the spectral sequence $$E_{2}^{pq} = H^{p}(BG, IH^{q}(X)) \Rightarrow IH_{G}^{p+q}(X)$$ converging to $IH^{*}(E_{n}G \times _X{G})$ degenerates at the $E_2$ term.

This is because of decomposition?

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I suspect this question would be acceptable at MathOverflow. –  Akhil Mathew Jul 20 '11 at 18:12
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