  The purpose of this note is to give an overview of our work on defining
algebraic counterparts for W. Chen and Y. Ruan's Gromov-Witten Theory of
orbifolds. This work will be described in detail in a subsequent paper.
  The presentation here is generally based on lectures given by two of us at
the Orbifold Workshop in Madison, Wisconsin. Following the spirit of the
workshop, we give a nontechnical introduction to stacks, a general discussion
of twisted stable maps, and a run-through of the issues that arise when
generalizing Gromov-Witten theory to Deligne-Mumford stacks.
  We make a special effort to make our constructions as canonical as we can,
systematically using the language of algebraic stacks. Our efforts bear some
concrete fruits; in particular, we are able to define the Chen-Ruan product in
degree 0 (the so called stringy cohomology of the stack) with integer
coefficients.
  Beware - this note may be vanishing in front of your eyes: first, a somewhat
less technical version intended for the workshop proceedings will shortly (we
hope) be submitted. Second, a much more detailed paper is in preparation, in
which all the technicalities which are swept under the rug here are discussed,
as well as some cool stuff about taking roots.
