Orbifold Zhu theory associated to intertwining operators

We study intertwining operators among the twisted modules for rational VOAs and show a new modular invariance of the space spanned by the trace functions associated to intertwining operators. Our result generalizes the results obtained by Zhu [J. Amer. Math. Soc. 9 (1996) 237–302], Dong, Li, and Mason [Commun. Math. Phys. 214 (2000) 1–56], and Miyamoto [q-alg/0010180].