2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124405We define a generalised Euler characteristic for arc-symmetric sets endowed with a group action. It coincides with equivariant homology for compact nonsingular sets, but is different in general. We lay emphasis on the particular case of $Z/2\Z$, and give an application to the study of the singularities of Nash function germs via an analog of the motivic zeta function of Denef & Loeser.20 pages, to appear in Ann. Inst. FourierAlgebraic Geometry14B05, 14P20, 14P25, 32S20text