  This is a continuation of the paper "Modular tensor categories and orbifold
theories", arXiv:math.QA/0104242. It discusses orbifold models of conformal
filed theory, or, in mathematical language, question of constructing the
category of representations of the fixed point algebra $V^G$ for a given vertex
operator algebra $V$ with an action of a finite group $G$. The previous paper
gave a proof of well-known conjecture of Dijkgraaf-Vafa-Verlinde-Verlinde
giving a complete answer to this question in the holomorphic case (when $V$ has
a unique simple module, $V$ itself) under the assumption that categories of
rrepresentations of $V$, $V^G$ are modular tensor categories. In the current
paper, we give a partial answer in non-holomorphic case. In particular, we show
that the category of representations of $V^G$ is completely determined by the
category of twisted $V$-modules together with the action of $G$ on this
category. Our approach is based on describing representations of $V$, $V^G$ and
relation between them in terms of tensor categories and avoids using the
technique of VOAs as much as possible.
