Commutative weakly invo-clean group rings

A ring $R$ is called weakly invo-clean if any its element is the sum or the difference of an involution and an idempotent. For each commutative unital ring $R$ and each abelian group $G$, we find only in terms of $R$, $G$ and their sections a necessary and sufficient condition when the group ring $R[G]$ is weakly invo-clean. Our established result parallels to that due to Danchev-McGovern published in J. Algebra (2015) and proved for weakly nil-clean rings.