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A nilmanifold is a quotient N\G of a connected and simply connected nilpotentLie group G by a uniform lattice N. In this paper we determine the Reidemeisterand Nielsen number of affine n-valued maps on such a nilmanifold. These aremaps for which a given lifting to G splits into n affine maps of the Lie groupG. In order to obtain this result we also establish a way of computing thenumber of generalized twisted conjugacy classes on finitely generated torsionfree nilpotent groups.

Nielsen numbers of affine n-valued maps on nilmanifolds