ScalingStacks

Proposition 3.7. Let $i:H\hookrightarrow G$ be a closed subgroup. Denote by $s:X\to G\times_{H}X,x\mapsto[e,x].$ If the anti-diagonal action of $H$ on $G\times X$ is free then there is an equivalence of categories

(3.6)

$\displaystyle(i,s)^{*}:\operatorname{DM}_{G}(G\times_{H}X)\stackrel{{\scriptstyle\sim}}{{\to}}\operatorname{DM}_{H}(X).$