Categorical measures for finite group actions

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 not equal. also give an example related to Polishchuk Van den Bergh, certain condition this is indeed necessary.