2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223678We study the class of the classifying stack of a finite group in a Grothendieck group of algebraic stacks introduced previously. We show that this class is trivial in a number of examples most notably for all symmetric groups. We also give some examples where it is not trivial. The latter uses counterexamples of Saltman and Swan to the problem of Noether.23 pagesAlgebraic Geometry20D99, 14L30text