2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63352We define motivic multiple polylogarithms and prove the double shuffle relations for them. We use this to study the motivic fundamental group of the multiplicative group - {N-th roots of unity} and relate it to geometry of modular varieties. In particular we get new information about the actionof the Galois group on the pro-l completion of the above fundamental group. This paper is the second part of "Multiple polylogarithms and mixed Tate motives" math.AG/0103059103 pages, corrected version, sections 3.5 and 10.4 addedAlgebraic GeometryNumber Theorytext