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

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