Twisted stable maps to tame Artin stacks

We develop the theory of twisted stable maps into a tame Artin stack M. We show that the stacks K(g,n)(M) of twisted stable maps are algebraic, and proper and quasi-finite over the corresponding stacks K(g,n)(M) of stable maps of the coarse moduli space M of M. In the special case where M = BC, the classifying stack of a linearly reductive group scheme G, we show that K(g,n)(BG) -> (M) over bar (g,n) is a flat morphism with local complete intersection fibers.