  We discuss properties of complex algebraic orbifold groups, their
characteristic varieties, and their abelian covers. In particular, we deal with
the question of (quasi)-projectivity of orbifold groups. We also prove a
structure theorem for the variety of characters of normal-crossing
quasi-projective orbifold groups. Finally, we extend Sakuma's formula for the
first Betti number of abelian covers of orbifold fundamental groups. Several
examples are presented, including a compact orbifold group which is not
projective and a Zariski pair of plane projective curves that can be told by
considering an unbranched cover of the projective plane with an orbifold
structure.
