In my talk, I will describe the operad (of parenthesized braids) PaB introduced originally by Dror Bar-Natan (in 1998). I will show that the pro-algebraic version of Grothendieck-Teichmueller group GT can be defined as the group of automorphisms of this operad. This statement was essentially proved by Dror Bar-Natan (in 1998). I would like to understand a pro-finite version of this statement and its relation to a question of Yasutaka Ihara posed in his ICM talk in 1990.