There is a Chern character from K-theory to negative cyclic homology. We show that it preserves the decomposition coming from Adams operations, at least in characteristic zero.

The K-theory of a polynomial ring R[t] contains the K-theory of R as a summand. For R commutative and containing ℚ, we describe K *(R[t])/K *(R) in terms of Hochschild homology and the cohomology of Kähler differentials for the cdh topology. We use this to address Bass’ question, whether K n (R)=K n (R[t]) implies K n (R)=K n (R[t 1,t 2]). The answer to this question is affirmative when R is essentially of finite type over the complex numbers, but negative in general.