  In this work we discuss the deformed relativistic wave equations, namely the
Klein--Gordon and Dirac equations in a Doubly Special Relativity scenario. We
employ what we call a geometric approach, based on the geometry of a curved
momentum space, which should be seen as complementary to the more spread
algebraic one. In this frame we are able to rederive well-known algebraic
expressions, as well as to treat yet unresolved issues, to wit, the explicit
relation between both equations, the discrete symmetries for Dirac particles,
the fate of covariance, and the formal definition of a Hilbert space for the
Klein--Gordon case.
