  We 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.
