k1-injectivity of the Paschke dual algebra for certain simple C*-algebras

Let B be a nonunital separable simple stable C*-algebra with strict comparison of positive elements and T (B) having finite extreme boundary, and let A be a simple unital separable nuclear C*-algebra. We prove that the Paschke dual algebra AB is K1-injective. As a consequence, we obtain interesting KK-uniqueness theorems which generalize the Brown–Douglas–Fillmore essential codimension property.