Orbifold conjecture for twisted intertwining operators

Let $V$ be a vertex operator algebra satisfying the following conditions: $V$ is simple, $V_{(0)}=\mathbb{C}\mathbf{1}$, $V_{(n)}=0$ for $n<0$, and the contragredient $V'$ is equivalent to $V$ as a $V$-module; $V$ is $C_{2}$-cofinite, meaning that $\dim V/C_{2}(V)<\infty$, where $C_{2}(V)$ is spanned by $\operatorname{Res}_{x}x^{-2}Y(u,x)v$ for $u,v\in V$; and every grading-restricted generalized $V$-module is completely reducible. Let $G$ be a finite group of automorphisms of $V$.

Twisted intertwining-operator conjecture. The twisted intertwining operators among the $g$-twisted $V$-modules, for all $g\in G$, satisfy associativity, commutativity and modular invariance.

This is presented as a main conjecture for orbifold conformal field theory and is intended to provide the structural properties needed to construct the orbifold theory. The supplied text gives no resolution evidence.