Mobility of a hexarotor UAV in its standard configuration is limited, since all the propeller force vectors are parallel and they achieve only 4-DoF actuation, similar, e.g., to quadrotors. As a consequence, the hexarotor pose cannot track an arbitrary trajectory while the center of mass is tracking a position trajectory. In this paper, we consider a different hexarotor architecture where propellers are tilted, without the need of any additional hardware. In this way, the hexarotor gains a 6-DoF actuation which allows to independently reach positions and orientations in free space and to be able to exert forces on the environment to resist any wrench for aerial manipulation tasks. After deriving the dynamical model of the proposed hexarotor, we discuss the controllability and the tilt angle optimization to reduce the control effort for the specific task. An exact feedback linearization and decoupling control law is proposed based on the input-output mapping, considering the Jacobian and task acceleration, for non-linear trajectory tracking. The capabilities of our approach are shown by simulation results.