Künneth theorem for complex K-theory with an even-cell factor
= Künneth theorem for complex K-theory with an even-cell factor
{c}
If $Y$ is a finite even-cell complex, the exterior product is an isomorphism
$$
K^0(Y)\otimes K^i(X)\xrightarrow{\ \cong\ }K^i(Y\times X).
$$
Cellular induction proves this because $K^0(Y)$ is free and $K^{-1}(Y)=0$.