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The forgetful functor from $D^b_G(X)$ to $D^b(X)$ carries $Perv_G(X)$ to $Perv(X)$ by definition $5.1$ in the book of Bernstein and Lunts. My question is do the following functors, intermediate extension, kernel and cokernel commute with forgetful functor?

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  • $\begingroup$ I don’t think so, since intersection homology and equivariant intersection homology are different, see the part of Bernstein and Lunts where they discuss intersection homology of toric varieties. $\endgroup$
    – Avi Steiner
    Commented Feb 4, 2019 at 15:33

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