  We show that there exists a purely infinite AH-algebra. The AH-algebra arises
as an inductive limit of C*-algebras of the form C_0([0,1),M_k) and it absorbs
the Cuntz algebra O_\infty tensorially. Thus one can reach an
O_\infty-absorbing C*-algebra as an inductive limit of the finite and
elementary C*-algebras C_0([0,1),M_k).
  As an application we give a new proof of a recent theorem of Ozawa that the
cone over any separable exact C*-algebra is AF-embeddable, and we exhibit a
concrete AF-algebra into which this class of C*-algebras can be embedded.
