Given a variety with finite group action, we compare its equivariant categorical measure, that is, the measure of corresponding quotient stack, and extended quotient. Using weak factorization for orbifolds, show wide range cases these two measures coincide. This implies, in particular, conjecture Galkin Shinder on motivic zeta-functions varieties. We provide examples showing that, general, are ...

Working over an algebraically closed field k, we prove that all orbits of a left action algebraic group superscheme G on X finite type are locally closed. Moreover, such orbit Gx, where x is k-point X, if and only Gevx in Xev, or equivalently, Gresx Xres. Here Gev the largest purely even super-subscheme Gres regarded as scheme. Similarly, Xev Xres We also sdim(Gx)=sdim(G)−sdim(Gx), Gx stabilize...