Let the finite group $G$ act on a vertex algebra $V$. It is expected that there are certain vector spaces $V_g$ (with the structure of $g$ twisted $V$ modules), with $V_1=V^G$, and $$V/G\ :=\ \bigoplus_{g\in G}V_g$$ has a vertex algebra structure.

I think the idea is that, if $V$ is a chiral quantisation of the jet space $J_\infty X$ of a scheme $X$, then $V/G$ is the chiral quantisation of the quotient stack $X/G$, $J_\infty(X/G)$.

**Question:** What is the current status of the construction of $V/G$? When is it expected to exist?

E.g. in Frenkel-Ben Zvi 5.7.1, it is claimed that there is a construction when $V$ is holomorphic and $G$ is cyclic. But I am wondering if there have been advances since then.