  The purpose of this paper is to study finite dimensional equivariant moduli
problems from the viewpoint of stratification theory. We show that there exists
a stratified obstruction system for a finite dimensional equivariant moduli
problem. In addition, we define a coindex for a G-vector bundle which is
determined by the G-action on the vector bundle and prove that if the coindex
of an oriented equivariant moduli problem is bigger than 1, then we obtain an
invariant Euler cycle via equivariant perturbation. In particular, we get a
localization formula for the stratified transversal intersection of S1-moduli
problems.
