A remark on a result of Huber and Kahn

Abstract

A. Huber and B. Kahn construct a relative slice filtration on the motive M(X) associated to a principal T-bundle X over a smooth scheme Y. As a consequence of their result, one can observe that the mixed Tateness of the motive M(Y) implies that the motive M(X) is mixed Tate. In this note we prove the inverse implication for a principal G-bundle, for a split reductive group G.