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A. Huber and B. Kahn construct a relative slice filtration on the motive M(X) associated to a principal T-bundle X over Y for a smooth scheme Y. As a consequence of
4 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.
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