The fibred category $\mathcal A$ of algebraic spaces over a scheme $S$ is a stack (over the category of affine schemes with the etale topology). This is proved in Laumon and Moret-Bailly's book (see (1.6.4) and (3.4.6)).

Let $\mathcal G$ be the fibred category of **group** algebraic spaces over a scheme $S$. Is $\mathcal G$ a stack?

My guess is that the forgetful functor $\mathcal G\to \mathcal A$ is "representable" in some sense (as the stabilizers of $\mathcal G$ are smaller than those of $\mathcal A$). But I can't see how to make this rigorous.

**Sidenote.** Note that $\mathcal A$ is not an algebraic stack (see Claim 3.1 in http://arxiv.org/pdf/math/0602646v1.pdf).