  Let $\mathcal{X}_1$ and $\mathcal{X}_2$ be smooth proper Deligne-Mumford
stacks with projective coarse moduli spaces. We prove a formula for orbifold
Gromov-Witten invariants of the product stack $\mathcal{X}_1\times
\mathcal{X}_2$ in terms of Gromov-Witten invariants of the factors
$\mathcal{X}_1$ and $\mathcal{X}_2$. As an application, we deduce a
decomposition result for Gromov-Witten theory of trivial gerbes.
