G-crossed tensor-category conjecture for twisted modules

Let $V$ be a vertex operator algebra satisfying the first two conditions of the twisted intertwining-operator conjecture: $V$ is simple with $V_{(0)}=\mathbb{C}\mathbf{1}$, $V_{(n)}=0$ for $n<0$, contragredient $V'\cong V$, and $V$ is $C_{2}$-cofinite. Let $G$ be a finite group of automorphisms of $V$. Consider the category whose objects are grading-restricted generalized $g$-twisted $V$-modules for all $g\in G$.

G-crossed tensor-category conjecture. This category has a natural structure of a $G$-crossed tensor category satisfying additional properties.

The conjecture extends the expected orbifold tensor-category structure beyond the completely reducible setting. The supplied text gives no resolution evidence.