Anabelian representations of the motivic Galois group

I will report on recent work concerning the action of the motivic Galois group on Anabelian objects such as fundamental groups of algebraic varieties conveniently completed. I’ll sketch the proof of a motivic analog of a theorem of Pop (aka., the Ihara-Matsumoto-Oda conjecture) yielding several interpretations of the motivic Galois group as the automorphism group of some large diagrams of anabelian objects.