  A universal coefficient theorem in the setting of Kirchberg's ideal-related
KK-theory was obtained in the fundamental case of a C*-algebra with one
specified ideal by Bonkat and proved there to split, unnaturally, under certain
conditions. Employing certain K-theoretical information derivable from the
given operator algebras in a way introduced here, we shall demonstrate that
Bonkat's UCT does not split in general. Related methods lead to information on
the complexity of the K-theory which must be used to classify *-isomorphisms
for purely infinite C*-algebras with one non-trivial ideal.
