  These lecture notes cover four topics. There is a proof of the fact that the
functors represented by the motivic Eilenberg-Maclane spaces on the motivic
homotopy category coincide with the motivic cohomology defined in terms of the
motivic complexes. There is a description of the equivariant motivic homotopy
category for a finite flat group scheme (over a noetherian base) together with
a new characterization of A^1-equivalences. There is a part where we introduce
a class of sheaves called solid sheaves. Finally there is a part where we study
functors of the form X -> X/G and X -> X^W and show that they preserve
equivalences between term-wise ind-solid simplicial sheaves.
