  We define Gromov-Witten classes and invariants of smooth proper tame
Deligne-Mumford stacks of finite presentation over a Dedekind domain. We prove
that they are deformation invariants and verify the fundamental axioms. For a
smooth proper tame Deligne-Mumford stack over a Dedekind domain, we prove that
the invariants of fibers in different characteristics are the same. We show
that genus zero Gromov-Witten invariants define a potential which satisfies the
WDVV equation and we deduce from this a reconstruction theorem for genus zero
Gromov-Witten invariants in arbitrary characteristic.
