Elliptic-reflection functor conjecture for orbifold surfaces

Let $[E/\Gamma]$ be the orbifold curve, let $\Xi$ denote the deformation data, and let $IW_R^{ell}$ act on $HH_0(E)$. Elliptic-reflection functor conjecture. There is a group $G$ acting on

$$D_{\operatorname{Coh}}(\mathbb P_{[E/\Gamma]_S]}(\Xi))$$

and an action

$$\rho:G\longrightarrow \operatorname{End}(HH_0([E/\Gamma]))$$

such that each $g\in G$ becomes $S$-linear after base change along $\rho(g)$, and the map $\rho$ factors through the action of $IW_R^{ell}$ on $HH_0(E)$. This is proposed as the extension of the proved non-orbifold reflection-functor construction to the other cases; the supplied text gives no resolution.