  We compute explicitly the Chow motive of any generalized Kummer variety
associated to any abelian surface. In fact, it lies in the rigid tensor
subcategory of the category of Chow motives generated by the Chow motive of the
underlying abelian surface. One application of this calculation is to show that
the Hodge conjecture holds for arbitrary products of generalized Kummer
varieties. As another application, all numerically trivial 1-cycles on
arbitrary products of generalized Kummer varieties are smash-nipotent.
