International audienceThe Rossby-Wave Instability (RWI) has been proposed to be at the origin of the highfrequency QPOs observed in black-hole systems. Here we are presenting the first full GR simulations of the instability around a Kerr black-hole which allow us to explore the impact of the spin on the instability. Those simulations, coupled with a full GR ray-tracing, allow us to directly compare our simulation with the observables we get through X-ray observations