Equivariant virtual Betti numbers

We define a generalised Euler characteristic for arc-symmetric sets endowed with a group action. It coincides with the Poincare series in equivariant homology for compact nonsingular sets, but is different in general. We put emphasis on the particular case of Z/2Z, and give an application to the study of the singularities of Nash function germs via an analog of the motivic zeta function of Denef and Loeser.