  In this note we describe very explicitly a rich family of mixed motives that
generates Voevodsky's $DM^{eff}_{gm}{\mathbb{Q}}$ (as a triangulated category).
They "should be" mixed since they have only one non-zero Betti cohomology
group. Our method also allows to define a family of direct summands of the
numerical motif of any smooth projective variety $P$. Modulo certain standard
conjectures, this construction yields the Kunneth decomposition of the diagonal
of $P$.
