On the ultrafilter semigroup of a topological group

The ultrafilter semigroup Ult(G) of a topological group G consists of all nonprincipal ultrafilters on G converging to the identity and is a closed subsemigroup in the Stone-Cech compactification beta G(d) of G as a discrete semigroup. We show that it is consistent with ZFC that for every countable nondiscrete topological group G, Ult(G) can be partitioned into closed right ideals each of which admits a continuous homomorphism onto the Bohr compactification of the integers.