Monomial Resolutions

We introduce the notion of a monomial resolution of a module over a group algebra, a construction which behaves similar to the projective resolution, but uses monomial modules instead. Over the complex numbers it is shown that, on the level of Grothendieck groups, the monomial resolution induces the canonical Brauer induction formula which was introduced in R. Boltje (Astérisque181–182 (1990), 31–59).