  We show that a new multiplicative genus, in the sense of Hirzebruch, can be
obtained by generalizing a calculation due to Atiyah and Witten. We introduce
this as the $\hat{\Gamma}$-genus, compute its value for some examples and
highlight some of its interesting properties. We also indicate a connection
with the study of multiple zeta values, which gives an algebraic interpretation
for our proposed regularization procedure.
