  We study complex-analytic properties of the augmented Teichmuller spaces ATS
introduced by Lipman Bers. These spaces are obtained by adding to the classical
Teichmuller space TS the points corresponding to nodal Riemann surfaces. Unlike
TS, the space ATS is not a complex manifold (it is not even locally compact).
We prove however that the quotient of ATS by any finite index subgroup of the
Teichmuller modular group has a canonical structure of a complex orbifold.
Using this structure we construct natural maps from ATS to stacks of admissible
coverings of stable Riemann surfaces. This result is important for
understanding the cup-product in stringy orbifold cohomology. We also establish
some new technical results from the general theory of orbifolds which may be of
independent interest.
