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Suppose that $X$ is a stack, and $Y \to X$ is a $\mu_2$-gerbe. Is there any relationship between the integral Chow rings (in the sense of Edidin and Graham) of $X$ and $Y$?

(I assume they become isomorphic upon inverting $2$; the meat here is what happens at the prime $2$...)

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I have only recently come across your question. Do you actually mean a $\mu_2$-torsor ? –  Damian Rössler Mar 23 at 14:24
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