We prove that the Drinfeld center \(Z(\mathcal {C})\) of a pivotal finite tensor category \({\mathcal {C}}\) comes with the structure of a ribbon Grothendieck–Verdier category in the sense of Boyarchenko–Drinfeld. Phrased operadically, this makes \(Z(\mathcal {C})\) into a cyclic algebra over the framed \(E_2\) -operad. The underlying object of the dualizing object is the distinguished invertible object of \({\mathcal {C}}\) appearing in the well-known Radford isomorphism of Etingof–Nikshych–Ostrik. Up to equivalence, this is the unique ribbon Grothendieck–Verdier structure on \(Z(\mathcal {C})\) extending the canonical balanced braided structure that \(Z(\mathcal {C})\) already comes equipped with. The duality functor of this ribbon Grothendieck–Verdier structure coincides with the rigid duality if and only if \({\mathcal {C}}\) is spherical in the sense of Douglas–Schommer-Pries–Snyder. The main topological consequence of our algebraic result is that \(Z(\mathcal {C})\) gives rise to an ansular functor, in fact even a modular functor regardless of whether \({\mathcal {C}}\) is spherical or not. In order to prove the aforementioned uniqueness statement for the ribbon Grothendieck–Verdier structure, we derive a seven-term exact sequence characterizing the space of ribbon Grothendieck–Verdier structures on a balanced braided category. This sequence features the Picard group of the balanced version of the Müger center of the balanced braided category.
