This paper presents a novel paradigm for physical interactive tasks in aerial robotics allowing to increase reliability and decrease weight and costs compared to state of the art approaches. By exploiting its tilted propeller actuation, the robot is able to control the full 6D pose (position and orientation independently) and to exert a full-wrench (force and torque independently) with a rigidly attached end-effector. Interaction is achieved by means of an admittance control scheme in which an outer loop control governs the desired admittance behavior (i.e., interaction compliance/stiffness, damping, and mass) and an inner loop based on inverse dynamics ensures full 6D pose tracking. The interaction forces are estimated by an IMU-enhanced momentum-based observer. An extensive experimental campaign is performed and four case studies are reported. Firstly, a hard touch and slide on a wooden surface, named sliding surface task. Secondly, a tilted peg-in-hole task, i.e., the insertion of the end-effector in a tilted funnel. Then an admittance shaping experiment in which it is shown how the stiffness, damping, and apparent mass can be modulated at will. Finally, the fourth experiment is in charge of showing the effectiveness of the approach also in the presence of time-varying interaction forces.