On unital absorbing extensions of C*-algebras of stable rank one and real rank zero

Suppose that B B is a separable stable C ∗ C^* -algebra with real rank zero, stable rank one and ( K 0 ( B ) , K 0 + ( B ) ) (\mathrm {K}_0(B), \mathrm {K}_0^+(B)) is weakly unperforated in the sense of Elliott [Internat. J. Math. 1 (1990), no. 4, pp. 361–380]. Let A A be a unital simple separable nuclear C ∗ \mathrm {C}^* -algebra. We show that B B has the corona factorization property and any unital extension of A A by B B is absorbing.