  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).
