Kaplansky's idempotent conjecture for group rings

Let $R$ be an integral domain and let $G$ be a torsionfree group. An idempotent in the group ring $RG$ is an element $e$ satisfying $e^2=e$. Kaplansky's conjecture. Every idempotent of $RG$ is trivial, namely equal to $0$ or $1$. This conjecture predicts the absence of nontrivial idempotents in group rings of torsionfree groups. The source gives several positive cases, including results for word-hyperbolic groups and additional cases under Farrell–Jones hypotheses, but the general statement remains open.