  Let (G,G^+) be a simple ordered abelian group. We say that G has strong
perforation if there exists a non-positive element x in G such that nx is
positive and non-zero for some natural number n. Otherwise, the group is said
to be weakly unperforated. Examples of simple C*-algebras whose ordered
K_0-groups have this property and for which the entire order structure on K_0
is known have, until now, been restricted to the case where K_0 is group
isomorphic to the integers. We construct simple, separable, unital C*-algebras
with strongly perforated K_0-groups group isomorphic to an arbitrary infinitely
generated subgroup of the rationals, and determine the order structure on K_0
in each case.
