  We consider Rota-Baxter algebras of meromorphic forms with poles along a
(singular) hypersurface in a smooth projective variety and the associated
Birkhoff factorization for algebra homomorphisms from a commutative Hopf
algebra. In the case of a normal crossings divisor, the Rota-Baxter structure
simplifies considerably and the factorization becomes a simple pole
subtraction. We apply this formalism to the unrenormalized momentum space
Feynman amplitudes, viewed as (divergent) integrals in the complement of the
determinant hypersurface. We lift the integral to the Kausz compactification of
the general linear group, whose boundary divisor is normal crossings. We show
that the Kausz compactification is a Tate motive and that the boundary divisor
and the divisor that contains the boundary of the chain of integration are
mixed Tate configurations. The regularization of the integrals that we obtain
differs from the usual renormalization of physical Feynman amplitudes, and in
particular it may give mixed Tate periods in some cases that have non-mixed
Tate contributions when computed with other renormalization methods.
