On the Motive of a Fibre Bundle and its Applications

Abstract

In this article we compute the motive associated to a cellular fibration $\Gamma$ over a smooth scheme $X$ inside Veovodsky's motivic categories. We implement this result to study the motive associated to a $G$-bundle, and additionally to study motives of varieties admitting a resolution of singularities by a tower of cellular fibrations (e.g. affine Schubert varieties in a twisted affine flag variety).

arXiv comment20 pages. arXiv admin note: substantial text overlap with arXiv:1112.4110