We recover some recent results by Dotsenko, Shadrin, and Vallette on the Deligne groupoid of a pre-Lie algebra, showing that they follow naturally by a pre-Lie variant of the PBW theorem. As an application, we show that Kapranov's L ∞ algebra structure on the Dolbeault complex of a K ähler manifold is homotopy abelian and independent on the choice of K ähler metric up to an L ∞ isomorphism, making the trivializing homotopy and the L ∞ isomorphism explicit.