I am a bit confused with the notation for the Chern character's domain and codomain.
Hatcher: https://www.math.cornell.edu/~hatcher/VBKT/VB.pdf defines ch: K(X) $\rightarrow$ $H^{*}(X,\mathbb{Z})$ where the RHS (codomain) should be a direct sum of even degree cohomology groups.
Is it true that the RHS (codomain) of ch can also be the Chow ring?
As for the LHS, K(X) is defined as in page 39.
In this article K(X) is denoted $K_1(X)$ sometimes I've seen $K_0(X)$ as well. What does $K_i(X)$ mean in this context?