A virtual fundamental class construction for the moduli space of (C*)n-equivariant morphisms

Let X be a smooth projective variety with the action of (C*)n. The article describes the moduli space of (C*)n equivariant morphisms from stable toric varieties into X as the inverse limit of the GIT quotients of X and their flips when these spaces are enhanced with a naturally associated Deligne-Mumford stack structure. This description is used for constructing a class in the Chow group of the moduli space of dimension dim(X) - n which is invariant under equivariant deformations of X.