  In this article, we give a proof of multiplicativity for $\gamma$-factors, an
equality of parabolically induced and inducing factors, in the context of the
Braverman-Kazhdan/Ngo program, under the assumption of commutativity of the
corresponding Fourier transforms and a certain generalized Harish-Chandra
transform. We also discuss the resolution of singularities and their
rationality for reductive monoids, which are among the basic objects in the
program.
