Hirzebruch formula conjecture for signatures of quotient spaces

Let $M$ be a manifold with a proper action of a discrete group $G$, and let $M/G$ be its quotient. Write $L(M)$ for the Hirzebruch $L$-class of $M$, and let $[M/G]$ denote the rational fundamental class of the quotient. The signature is

$$\operatorname{sign}(M/G)=\operatorname{sign} H^{*}(M/G;\mathcal{Q})\in\mathbb{Z}.$$

Hirzebruch formula conjecture. The signature satisfies

$$\operatorname{sign}(M/G)=\langle L(M),[M/G]\rangle\in\mathcal{Q}.$$

The quotient $M/G$ satisfies Poincare duality in homology with rational coefficients, so its signature is defined. The conjecture proposes an analogue of the Hirzebruch signature formula for quotients by proper group actions.