We extend the definition of the Chen-Ruan cohomology ring to smooth, proper, tame, Deligne-Mumford stacks over fields of positive characteristic and prove that a modified version of the Frobenius action preserves the product.
Comment: Updated to match version published in Communication in Number Theory and Physics, 2007. Conjecture 6.3 has been replaced with a Theorem following the work of Yasuda. The title of the article has been updated