UV dimensional reduction to two from group valued momenta

We describe a new model of deformed relativistic kinematics based on the group manifold U(1)×SU(2) as a four-momentum space. We discuss the action of the Lorentz group on such space and illustrate the deformed composition law for the group-valued momenta. Due to the geometric structure of the group, the deformed kinematics is governed by two energy scales λ and κ. A relevant feature of the model is that it exhibits a running spectral dimension ds with the characteristic short distance reduction to ds=2 found in most quantum gravity scenarios.