Transferring homotopy commutative algebraic structures

We show that the sum over planar tree formula of Kontsevich and Soibelman transfers C∞C∞-structures along a contraction. Applying this result to a cosimplicial commutative algebra A•A• over a field of characteristic zero, we exhibit a canonical C∞C∞-structure on Tot(A•)Tot(A•), which is unital if A•A• is; in particular, we obtain a canonical C∞C∞-structure on the cochain complex of a simplicial set.