Standard quadrotor UAVs possess a limited mobility because of their inherent underactuation, i.e., availability of 4 independent control inputs (the 4 propeller spinning velocities) vs. the 6 dofs parameterizing the quadrotor position/ orientation in space. As a consequence, the quadrotor pose cannot track an arbitrary trajectory over time (e.g., it can hover on the spot only when horizontal). In this paper, we propose a novel actuation concept in which the quadrotor propellers are allowed to tilt about their axes w.r.t. the main quadrotor body. This introduces an additional set of 4 control inputs which provides full actuation to the quadrotor position/orientation. After deriving the dynamical model of the proposed quadrotor, we formally discuss its controllability properties and propose a nonlinear trajectory tracking controller based on dynamic feedback linearization techniques. The soundness of our approach is validated by means of simulation results.