  In this paper, we prove that the group of homotopy automorphisms of the
profinite completion of the operad of little $2$-disks is isomorphic to the
profinite Grothendieck-Teichm\"uller group. In particular, the absolute Galois
group of $\mathbb{Q}$ acts faithfully on the profinite completion of $E_2$ in
the homotopy category of profinite weak operads.
