Let $G$ be any group. $R$ is a $Z$-module. Let $G_{SpecR}=\amalg_{g\in G}SpecR$. I see that $G_{SpecR}\times_{SpecZ}G_{Spec R} $ is isomorphic with $\amalg_{g,g^{'}\in G}SpecR$ from the note "finite group scheme".My question is
1)Why they are isomorphic ? What is the isomorphic map?
2)Since they are isomorphic ,I guess that the elements of $G_{SpecR}\times_{SpecZ}G_{Spec R} $ look like $"a\times a"$ .Is it true? If it is ture,why the elements are not $"a\times b"$?