Polya's conjecture for Dirichlet domains of cocompact group actions

Let $M$ be a complete, contractible Riemannian manifold, and let a group $\Gamma$ act properly, effectively, and cocompactly on $M$ by isometries. A Dirichlet domain of $\Gamma$ is a fundamental domain associated with this action. Manifold generalization of Polya's conjecture. Every Dirichlet domain of $\Gamma$ satisfies Pólya's conjecture for both Neumann and Dirichlet eigenvalues. This proposes extending Pólya's spectral inequalities from Euclidean domains to Dirichlet domains in cocompact geometric actions; the source does not give a resolution status.