For an action of a finite group G on a compact manifold X one can define the `orbifold Euler characteristic' e(X,G) as \(\frac{1}{| G|}\sum e(X^{}) \), where summation runs over all commuting pairs (g,h) in G and \(e(X^{})\) is the topological Euler characteristic of the common fixed point set. This invariant has been introduced in string theory. We suspect that if X is a complex manifold, G operates trivially on its canonical bundle and X/G has some good resolution of singulariies not affecting the canonical bundle, then e(X,G) equals the topological Euler characteristic of this resolution. We mention some relations to loop spaces and equivariant K-theory and check our guess in some examples from algebraic geometry. In particular we consider the Hilbert scheme of \(n\quad points\) on an algebraic surface which is a good resolution of the n-th symmetric power of the surface. The Betti numbers of this resolution have been computed by \textit{L. Göttsche} [``The Betti numbers of the Hilbert scheme of points on a smooth projective surface``, Math. Ann. (to appear; see the following review)].