$G$-crossed braided tensor categories of twisted modules

Let $V$ be a strongly rational vertex operator algebra and $G\le \mathrm{Aut}(V)$ a finite group. We prove Huang’s conjecture that the categories of $g$-twisted $V$-modules, for $g\in G$, form a $G$-crossed braided fusion category. This category is faithfully $G$-graded, with tensor products representing the complete twisted intertwining operators of Du-Huang, the canonical pullback $G$-action, and crossed braiding. In particular, the associativity, coherence and rigidity required by the conjecture all hold.