Riemann-Roch for Deligne-Mumford stacks
  We give a simple proof of the Riemann-Roch theorem for Deligne-Mumford stacks using the equivariant Riemann-Roch theorem and the localization theorem in equivariant K-theory together with some basic commutative algebra of Artin rings. 
Dan Edidin
math.AG math.KT