The twisted Selberg trace formula and the Selberg zeta function for compact orbifolds

We study elements of the spectral theory of compact hyperbolic orbifolds $\mathrm{\Gamma }\mathrm{\backslash }{\mathbb{H}}^n$. We establish a version of the Selberg trace formula for non-unitary representations of $\mathrm{\Gamma }$ and prove that the associated Selberg zeta function admits a meromorphic continuation to $\mathbb{C}$.