Automorphism groups of elliptic G-structures on orbifolds

We present a new method of investigation of G-structures on orbifolds. This method is founded on the use of appropriate G-structure on an associated model manifold. Applying this method we prove the existence and the uniqueness of finite dimensional Lie group structures on the full automorphism group of an elliptic G-structure on a compact orbifold. This generalizes the well-known theorem for elliptic G-structures on compact manifolds. As an application we get that the group of all automorphisms of an almost complex structure on a compact orbifold is a finite dimensional Lie group that carries a uniquely defined Lie group structure.