A Remark on a Result of Huber and Kahn

A. Huber and B. Kahn construct a relative slice filtration on a principal T-bundle X over Y, for smooth Y. As a consequence of their result, one can observe that the mixed Tateness of the motive M(Y), associated to the smooth scheme 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.