Kernel of the Adams operation on the algebraic K-theory

Question

Adams operation $\psi^n$ acts on the algebraic $K$-theory groups of a commutative ring $R$. Its known that eigenvalues of $\psi^n$ on $\mathbb{Q}\otimes K_i(R)$ can only be non-negative powers of $n$. Especially it doesn't have any non-trivial elements in the kernel rationally. Is it possible for $\psi^n$ to have a non-trivial element in kernel as a map from $K_i(R)$ to itself? I think it should be possible. I do not have a good intuition why the eigenvalues can only be powers of $n$ any explanation for that part is also welcome.