  We prove an explicit formula for the total Chern character of the Verlinde
bundle over the moduli space of pointed stable curves in terms of tautological
classes. The Chern characters of the Verlinde bundles define a semisimple CohFT
(the ranks, given by the Verlinde formula, determine a semisimple fusion
algebra). According to Teleman's classification of semisimple CohFTs, there
exists an element of Givental's group transforming the fusion algebra into the
CohFT. We determine the element using the first Chern class of the Verlinde
bundle on the moduli space of nonsingular curves and the projective flatness of
the Hitchin connection.
