Periods and mixed motives
  We 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/0103059 
A. B. Goncharov