Let $R$ be a commutative unital ring, let $G$ be a group and let $R[G]$ its group $R$-algebra.
- It is true that $\mathbb{Z}[G]\otimes_{\mathbb{Z}}R\simeq R[G]$?
- If not, there are conditions on $R$ and $G$ which ensure this?
Thank you and sorry if the question is too obvious.