Weak semiprojectivity in purely infinite simple C*-algebras

Let A be a separable amenable purely infinite simple C*-algebra which satisfies the Universal Coefficient Theorem. We prove that A is weakly semiprojective if and only if K-i(A) is a countable direct sum of finitely generated groups (i = 0, 1). Therefore, if A is such a C*-algebra, for any epsilon > 0 and any finite subset F subset of A there exist delta > 0 and a finite subset G subset of A satisfying the following: for any contractive positive linear map L : A --> B (for any C* -algebra B) with parallel to L(ab) - L(a)L(b)parallel to < delta for a, b is an element of G there exists a homomorphism h: A -> B such that parallel to h(a) - L(a)parallel to < epsilon for a is an element of T.