A Character on the Quasi-Symmetric Functions coming from Multiple Zeta Values

We define a homomorphism ζ from the algebra of quasi-symmetric functions to the reals which involves the Euler constant and multiple zeta values. Besides advancing the study of multiple zeta values, the homomorphism ζ appears in connection with two Hirzebruch genera of almost complex manifolds: the Γ-genus (related to mirror symmetry) and the Γ̂-genus (related to an S1-equivariant Euler class). We decompose ζ into its even and odd factors in the sense of Aguiar, Bergeron, and Sottille, and demonstrate the usefulness of this decomposition in computing ζ on the subalgebra of symmetric functions (which suffices for computations of the Γand Γ̂-genera).