  Let L be a finite field extension of Q_p and let G be the group of L-rational
points of a split connected reductive group over L. We view G as a locally
L-analytic group with Lie algebra g. We define a functor from admissible
locally analytic G-representations with prescribed infinitesimal character to a
category of equivariant sheaves on the Bruhat-Tits building of G. For smooth
representations, the corresponding sheaves are closely related to the sheaves
constructed by S. Schneider and U. Stuhler. The functor is also compatible, in
a certain sense, with the localization of g-modules on the flag variety by A.
Beilinson and J. Bernstein.
