  The cherry on top of this stacky paper is the following: for any g>1 we give
a finite group G such that the moduli space of connected admissible G-covers of
genus g is a smooth, fine moduli space, which is a Galois cover of the moduli
space of stable curves.
  The proof relies on methods introduced by Looijenga and Pikaart-De Jong, and
on the theory of twisted G-covers, a theory announced without proofs in
math.AG/9811059, section 3, and developed in the first few sections of this
paper. This includes a moduli description of the normalization of the
Harris-Mumford space of admissible covers, and a study of moduli of stable
curves with abelian and non-abelian level structure.
