The relationship between skew group algebras and orbifold theory

Let V be a simple vertex operator algebra and let G be a finite automorphism group of V. In [C. Dong, G. Yamskulna, Math. Z., to appear], it was shown that any irreducible V-module is a completely reducible VG-module where VG is the G-invariant vertex operator subalgebra of V. In this paper, we give an alternative proof of this fact using the theory of skew group algebras. We also extend this result to any irreducible g-twisted V-module when g is in the center of G and V is a g-rational vertex operator algebra.