Unobstructedness conjecture for quantized symplectic quotient algebras

Let $M$ be a symplectic $C^\infty$-manifold or an affine complex algebraic variety, let $G$ be a finite group acting on $M$ by symplectic transformations, and let $B$ be a $G$-equivariant quantization of $M$. Set

$$A_0=G\mathbin{\triangleright\!\!\!<}B[\hbar^{-1}].$$

The Hochschild cohomology satisfies

$$H^2(A_0)=\left(H^2(M)\oplus\mathbb C[S]\right)^G,$$

where $S$ is the set of pairs $(g,Y)$ such that $g\in G$ and $Y$ is a connected component of $M^g$ of codimension $2$. Unobstructedness conjecture. The deformations of the algebra $A_0$ are unobstructed. Thus there exists a universal deformation $H_c$ of this algebra parametrized by $c\in H^2(A_0)$. This conjecture predicts that the deformation theory of these quantized symplectic quotient algebras has no obstruction classes, despite the possible nonvanishing of $H^3(A_0)$.