  Let $G$ be a finite-dimensional Poisson algebraic, Lie or formal group. We
show that the center of the quantization of $G$ provided by an Etingof-Kazhdan
functor is isomorphic as an algebra to the Poisson center of the algebra of
functions on $G$. This recovers and generalizes Duflo's theorem which gives an
isomorphism between the center of the enveloping algebra of a
finite-dimensional Lie algebra $\mathfrak{a}$ and the subalgebra of
ad-invariant in the symmetric algebra of $\mathfrak{a}$. As our proof relies on
Etingof-Kazhdan construction it ultimately depends on the existence of Drinfeld
associators, but otherwise it is a fairly simple application of graphical
calculus. This shed some lights on Alekseev-Torossian proof of the
Kashiwara-Vergne conjecture, and on the relation observed by
Bar-Natan-Le-Thurston between the Duflo isomorphism and the Kontsevich integral
of the unknot.
