Geometric side of a local relative trace formula

International audienceFollowing a scheme suggested by B. Feigon, we investigate a local relative trace formula in the situation of a reductive p-adic group G relative to a symmetric subgroup H " HpF q where H is split over the local field F of characteristic zero and G " GpF q is the restriction of scalars of H IE relative to a quadratic unramified extension E of F. We adapt techniques of the proof of the local trace formula by J. Arthur in order to get a geometric expansion of the integral over H ˆ H of a truncated kernel associated to the regular representation of G. Mathematics Subject Classification 2000: 11F72, 22E50