Decomposition rank and absorbing extensions of type I algebras

In the case of infinite decomposition rank, we provide a counterexample. Specifically, we construct a unital, homogeneous, split exact sequence of the form0→C(Z)⊗K→C→C→0which is not absorbing. In this example, Z is an infinite-dimensional, compact, second countable topological space. This gives a counterexample to the natural infinite-dimensional generalization of the result of Pimsner, Popa and Voiculescu.