Twisted representations of conformal nets and crossed balanced tensor categories

Let $\mathcal{A}$ be a (not necessarily rational) conformal net with an action of a discrete group $G$. We show that the category ${\text{Rep}}^G(\mathcal{A})$ of $G$-twisted representations of $\mathcal{A}$ is canonically a $G$-crossed balanced ${\mathrm{W}}^{\ast }$-tensor category. This extends the results of Müger arXiv:math/0403322, in the language of localized endomorphisms, that ${\text{Rep}}^G(\mathcal{A})$ is a $G$-crossed braided tensor category.