Nonseparable CCR algebras

Extending a result of the first author and Katsura, we prove that for every UHF algebra $A$ of infinite type, in every uncountable cardinality $\kappa$ there are $2^{\kappa }$ nonisomorphic approximately matricial C*-algebras with the same $K_0$ group as $A$. These algebras are group \cstar-algebras `twisted’ by prescribed canonical commutation relations (CCR), and they can also be considered as nonseparable generalizations of noncommutative tori.