  In the recent literature one can find calculations of various one--loop
amplitudes, like anomalies, tadpoles and vacuum energies, on specific types of
orbifolds, like S^1/Z_2. This work aims to give a general description of such
one--loop computations for a large class of orbifold models. In order to
achieve a high degree of generality, we formulate these calculations as
evaluations of traces of operators over orbifold Hilbert spaces. We find that
in general the result is expressed as a sum of traces over hyper surfaces with
local projections, and the derivatives perpendicular to these hyper surfaces
are rescaled. These local projectors naturally takes into account possible
non--periodic boundary conditions. As the examples T^6/Z_4 and T^4/D_4
illustrate, the methods can be applied to non--prime as well as non--Abelian
orbifolds.
