# Stack cohomology vs cohomology of the quotient

Let $X$ be an affine scheme over an algebraically closed field $K$ of positive characteristic, $G$ a finite group acting on $X$, $[X/G]$ the quotient stack and $p:[X/G]\to X/G$ the natural map of stacks. The characteristic of $K$ may divide the order of $G$. Is it true that the adjunction map $\underline{\mathbb{Q}}_\ell\to p_*p^{-1}\underline{\mathbb{Q}}_\ell$ is an isomorphism (where $\ell\neq char K$ is a prime)?

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cat -- I've put backticks around the formula with an asterisk. – algori Jul 13 '11 at 18:18