### Riemann-Roch for algebraic stacks I, by Roy Joshua

In this paper we extend Thomason's descent spectral sequence for the
topological G-theory of algebraic stacks. Topological G-theory is defined as
a localization of algebraic G-theory by topological K-homology. Riemann-Roch
for all proper maps between algebraic stacks as a natural transformation
between algebraic and topological G-theory is an immediate corollary. We
conclude with a Lefschetz-Riemann-Roch theorem for torus actions on
Deligne-Mumford stacks.

Roy Joshua <joshua@math.ohio-state.edu>