  We construct a functor that associates to any dg cooperad of dg commutative
algebras (satisfying some conditions) an augmented commutative algebra. When
applied to the cohomology operad of Francis Brown's moduli spaces it produces
an algebra that formally models the algebra of multiple zeta values. We prove
that there is an injection from the graded dual of the
Grothendieck-Teichmueller Lie algebra into the indecomposables of the algebra
associated to the Gerstenhaber cooperad, and that there is a morphism from the
algebra associated to Brown's moduli spaces to the algebra associated to the
Gerstenhaber cooperad which is surjective on indecomposables.
