  A braided category of C*-algebras is constructed. Its objects are C*-algebras
endowed with an action of the group R, its morphisms are C*-algebras morphisms
intertwining the action of R, the crossed product of its two objects
essentially depends on the action of R on considered C*-algebras. Crossed
products of any object with the algebra of all continuous vanishing at infinity
functions on R and algebras of all continuous functions on one- and
twodimensional tori are discussed.
