Yet Another Description of the Connes—Higson Functor.

Suppose that A and B are C*-algebras, A is separable, and B is stable. The elements of the group E1(A, B) in Connes—Higson E-theory are represented by *-homomorphisms from the suspension of A to the asymptotic algebra 21B. In the paper, an endofunctor M in the category of C* -algebras is constructed and a set of special homotopy classes of *-homomorphisms from A to MUB is defined so that this set endowed with the natural structure of an Abelian group coincides with E1(A,B). [ABSTRACT FROM AUTHOR]