In this article we prove that the additive invariant co-represented by the noncommutative motive Z[r] is the Grothendieck group of endomorphisms functor K0End. Making use of Almkvist's foundational work, we then show that the ring Nat(K0End, K0End) of natural transformations (whose multiplication is given by composition) is naturally isomorphic to the direct sum of Z with the ring W0(Z[r]) of fractions of polynomials with coefficients in Z[r] and constant term 1.
Homology, Homotopy and Applications, Vol. 13 (2011), No. 2, pp.315-328.