  We consider a general McKean-Vlasov stochastic differential equation driven
by a rotationally invariant $\alpha$-stable process on $\mathbb{R}^d$ with
$\alpha \in (1,2)$. We assume that the diffusion coefficient is the identity
matrix and that the drift is bounded and H{\"o}lder continuous in some precise
sense with respect to both space and measure variables. The main goal of this
work is to prove new propagation of chaos estimates, at the level of semigroup,
for the associated mean-field interacting particle system. Our study relies on
the regularizing properties and the dynamics of the semigroup associated with
the McKean-Vlasov stochastic differential equation, which acts on functions
defined on $\mathcal{P}_\beta(\mathbb{R}^d)$, the space of probability measures
on $\mathbb{R}^d$ having a finite moment of order $\beta \in (1,\alpha)$. More
precisely, the dynamics of the semigroup is described by a backward Kolmogorov
partial differential equation defined on the strip $[0,T] \times
\mathcal{P}_\beta(\mathbb{R}^d)$.
