  We show that the Hopf algebra of quasi-symmetric functions arises naturally
as the integral Chow ring of the algebraic stack of expanded pairs originally
described by J. Li, using a more combinatorial description in terms of
configurations of line bundles. In particular, we exhibit a gluing map which
gives rise to the comultiplication. We then apply the result to calculate the
Chow rings of certain stacks of semistable curves.
