When $B$ is étale over $C$ and $A$ or $B$ is finite over $C$, then the result is known by Theorem (2.4) in my paper Descent for the $K$-theory of polynomial rings.
4 of 4
Updated the link, the previous one went to a 404 error page
Wilberd van der Kallen
- 3.5k
- 1
- 27
- 23