Abstract: A number of questions regarding closure properties of the class
of approximately homogeneous C*-algebras were resolved in the
negative by our examples with Dadarlat. Since these examples were
infinitely many ideals, this calls for determining whether good
closure properties can be found for C*-algebras with only finitely
We offer positive results in this direction, based on an analysis of
the interplay between the order on K-theory with coefficients and
the splitting maps for Künneth sequences provided by Bödigheimer.