  We consider the deformation of the Poincar\'e group in 2+1 dimensions into
the quantum double of the Lorentz group and construct Lorentz-covariant
momentum-space formulations of the irreducible representations describing
massive particles with spin 0, 1/2 and 1 in the deformed theory. We discuss
ways of obtaining non-commutative versions of relativistic wave equations like
the Klein-Gordon, Dirac and Proca equations in 2+1 dimensions by applying a
suitably defined Fourier transform, and point out the relation between
non-commutative Dirac equations and the exponentiated Dirac operator considered
by Atiyah and Moore.
