  We use an analogue of Karoubi's construction in the motivic situation to give
some cohomology operations in motivic cohomology. We prove many properties of
these operations, and we show that they coincide, up to some nonzero constants,
with the reduced power operations in motivic cohomology originally constructed
by Voevodsky. The relation of our construction to Voevodsky's is, roughly
speaking, that of a fixed point set to its associated homotopy fixed point set.
