  We put two C*-algebras together in a noncommutative tensor product using
quantum group coactions on them and a bicharacter relating the two quantum
groups that act. We describe this twisted tensor product in two equivalent
ways. The first construction is based on certain pairs of representations of
quantum groups which we call Heisenberg pairs because they generalise the Weyl
form of the canonical commutation relations. The second construction uses
covariant Hilbert space representations. We establish basic properties of the
twisted tensor product and study some examples.
