The orbifold elliptic genus conjecture for unramified finite group quotients

Let $X$ be a complex manifold equipped with an effective action of a finite group $G$. Write $X/G$ for the quotient, and let $\widehat{Ell}(X/G,;y,q)$ denote the normalized elliptic genus of the quotient. The orbifold elliptic genus is denoted by $Ell_{orb}(X,G;y,q)$, where $z$ and $\tau$ are related to $y$ and $q$ in the usual way. Orbifold elliptic genus conjecture. Then

$$Ell_{orb}(X,G;y,q)=\left(\frac{2\pi {\rm i}\theta(-z,\tau)}{\theta'(0,\tau)}\right)^{{\rm \dim} X}\widehat{Ell}(X/G,;y,q).$$

This is proposed in the case where the quotient map $X\to X/G$ has no ramification. It asserts that the orbifold elliptic genus of the global quotient agrees, up to the displayed normalization factor, with the elliptic genus of the quotient singularity.