Quantization commutes with reduction for b-symplectic manifolds

Let $(M,Z,\omega,\mu)$ be a compact connected Hamiltonian $G$-space, where $G$ is compact and connected, $M$ is prequantizable, and $Q_G(M,Z,\omega)\in R(G)$ is its equivariant quantization. If $0$ is a regular value of the moment map and

$$M_{\mathrm{red}}=\mu^{-1}(0)/G,\qquad Z_{\mathrm{red}}=(\mu^{-1}(0)\cap Z)/G$$

is a $b$-symplectic manifold or orbifold, with reduced form $\omega_{\mathrm{red}}$, then quantization commutes with reduction conjecture.

$$[Q_G(M,Z,\omega)]^G=Q(M_{\mathrm{red}},Z_{\mathrm{red}},\omega_{\mathrm{red}})\in\mathbb Z.$$

This is the $[Q,R]=0$ principle for $b$-symplectic manifolds: the invariant part of equivariant quantization should agree with the quantization of the reduced space. The source states the result as a conjecture under the regular-value and $b$-symplectic reduction hypotheses; no resolution is given.