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We prove that the Drinfeld center $Z(\mathcal{C})$ of a pivotal finite tensorcategory $\mathcal{C}$ comes with the structure of a ribbonGrothendieck-Verdier category in the sense of Boyarchenko-Drinfeld. Phrasedoperadically, this makes $Z(\mathcal{C})$ into a cyclic algebra over the framed$E_2$-operad. The underlying object of the dualizing object is thedistinguished invertible object of $\mathcal{C}$ appearing in the well-knownRadford isomorphism of Etingof-Nikshych-Ostrik. Up to equivalence, this is theunique ribbon Grothendieck-Verdier structure on $Z(\mathcal{C})$ extending thecanonical balanced braided structure that $Z(\mathcal{C})$ already comesequipped with. The duality functor of this ribbon Grothendieck-Verdierstructure coincides with the rigid duality if and only if $\mathcal{C}$ isspherical in the sense of Douglas-Schommer-Pries-Snyder. The main topologicalconsequence of our algebraic result is that $Z(\mathcal{C})$ gives rise to anansular functor, in fact even a modular functor regardless of whether$\mathcal{C}$ is spherical or not. In order to prove the aforementioneduniqueness statement for the ribbon Grothendieck-Verdier structure, we derive aseven-term exact sequence characterizing the space of ribbonGrothendieck-Verdier structures on a balanced braided category. This sequencefeatures the Picard group of the balanced version of the M\"uger center of thebalanced braided category.

The distinguished invertible object as ribbon dualizing object in the Drinfeld center