We recall the construction of non-formal deformation quantization of the Poincaré Group ISO(1,1) on its coadjoint orbit and exhibit the associated non-formal star-exponentials.
Bieliavsky, P., Marcillaud de Goursac, A., & Spinnler, F. (2013). Non-formal deformation quantization and star-exponential of the Poincare Group. Geometric Methods in Physics - XXXI Workshop, Białowieża, Poland, June 24–30, 2012, p. 3-12. https://hdl.handle.net/2078.5/223084