  By restricting the functional integration to the Regge geometries, we give
the discretized version of the well known path integral formulation of
2--dimensional quantum gravity in the conformal gauge. We analyze the role
played by diffeomorphisms in the Regge framework and we give an exact
expression for the Faddeev--Popov determinant related to a Regge surface; such
an expression in the smooth limit goes over to the correct continuum result.
