Deformation quantization for actions of Kählerian Lie groups

Let \mathbb{B} be a Lie group admitting a left-invariant negatively curved Kählerian structure. Consider a strongly continuous action \alpha of \mathbb{B} on a Fréchet algebra \mathcal{A}. Denote by \mathcal{A}^\infty the associated Fréchet algebra of smooth vectors for this action. In the Abelian case \mathbb{B}=\mathbb{R}^{2n} and \alpha isometric, Marc Rieffel proved that Weyl's operator symbol composition formula (the so called Moyal product) yields a deformation through Fréchet algebra structures \{\star_{\theta}^\alpha\}_{\theta\in\mathbb{R}} on \mathcal{A}^\infty. When \mathcal{A} is a