  Deligne's conjecture that $\ell$-adic sheaves on normal schemes over a finite
field admit $\ell'$-companions was proved by L. Lafforgue in the case of curves
and by Drinfeld in the case of smooth schemes. In this paper, we extend
Drinfeld's theorem to smooth Artin stacks and deduce Deligne's conjecture for
coarse moduli spaces of smooth Artin stacks. We also extend related theorems on
Frobenius eigenvalues and traces to Artin stacks.
