The Motivic DGA and applications.

In this talk we will outline the existence of an E_{infinity} structure
on the motivic complexes, motives of smooth schemes and on complexes
defining etale cohomology. The latter provides cohomology operations
in etale cohomology whereas the first provides classical cohomology
operations on motivic cohomology. We also compare Voevodsky's motivic
cohomology operations with these classical ones. Part of this is
joint work with Patrick Brosnan.