Left maximal idempotents in G⁎

Let G be a countably infinite discrete group, let βG be the Stone-Čech compactification of G, and let G⁎=βG∖G. The left (right) preordering on idempotents of G⁎ is defined by p≤Lq⇔pq=p (p≤Rq⇔qp=p). As any compact Hausdorff right topological semigroup, G⁎ has right maximal idempotents. We show (in ZFC) that there are left maximal idempotents in G⁎. In the case G=Z, this is the answer to a long standing question.