  We show that there is a family of complex semisimple Hopf algebras that do
not admit a Hopf order over any number ring. They are Drinfel'd twists of
certain group algebras. The twist contains a scalar fraction which makes
impossible the definability of such Hopf algebras over number rings. We also
prove that a complex semisimple Hopf algebra satisfies Kaplansky's sixth
conjecture if and only if it admits a weak order, in the sense of Rumynin and
Lorenz, over the integers.
