Algebraic K-theory of stable C∗-algebras

AbstractLet A be a unital C∗-algebra and let l denote the Calkin algebra (the bounded operators on a separable Hilbert space, modulo the compact operators K). We prove the following conjecture of M. Karoubi: the algebraic and topological K-theory groups of the tensor product C∗-algebra A ⊗ l are equal. The algebra A ⊗ l may be regarded as a “suspension” of the more elementary C∗-algebra A ⊗ K; thus Karoubi's conjecture asserts, roughly speaking, that the algebraic and topological K-theories of stable C∗-algebras agree