  We prove that the irreducible components of the characteristic varieties of
quasi-projective manifolds are either pull-backs of such components for
orbifolds, or torsion points. This gives an interpretation for the so-called
\emph{translated} components of the characteristic varieties, and shows that
the zero-dimensional components are indeed torsion. The main result is used to
derive further obstructions for a group to be the fundamental group of a
quasi-projective manifold.
