In this paper, we investigate Murre's conjectures on the structure of rational Chow groups and exhibit explicit Chow-Kunneth projectors for some examples. More precisely, the examples we study are the varieties which have a nef tangent bundle. For surfaces and threefolds which have a nef tangent bundle, explicit Chow-Kunneth projectors are obtained which satisfy Murre's conjectures, and the motivic Hard Lefschetz theorem is verified.
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