The Brauer group of quotient spaces by linear group actions

It is proved that for a smooth compactification of a quotient space of a linear space $V$ by the action of a linear algebraic group $G$, the Artin–Mumford birational invariant $\operatorname{Br}_v(V/G)=H^3(V/G,Z)_\text{tors}$ is effectively computable in terms of the 2-dimensional group cohomology $H^2(G,Q/Z)$ of $G$; examples of groups for which the invariant $\operatorname{Br}_v(V/G)$ is nontrivial are also studied.
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