Remark 5

Suppose that G is the product $G'\times G''$ of two finite groups. We define isomorphisms $\varphi_{G'}$ and $\varphi_{G''}$ as in the previous example.

We have a commutative diagram

$R_K(G')\otimes_{\mathbf{Z}}R_K(G'')^{\kappa}$ // $R_K(G)$

$\varphi_{G'}\otimes \varphi_{G''}\varphi_G$

$R_{K'}(G')\otimes_{\mathbf{Z}}R_{K'}(G'')^{\kappa'}$ // $R_{K'}(G)$,

where the isomorphisms $\kappa$ and $\kappa '$ are those defined in VIII, p. 406.