Witt vectors and K-theory of automorphisms via noncommutative motives

We prove that the functor ring-of-rational-Witt-vectors W_(−) becomes corepresentable in the category of noncommutative motives. As an application, we obtain an immediate extension of W_0(−) from commutative rings to schemes. Then, making use of the theory of noncommutative motives, we classify all natural transformations of the functor K-theory-of-automorphisms.