  We consider random walks on locally compact groups, extending the geometric
criteria for the identification of their Poisson boundary previously known for
discrete groups. First, we prove a version of the Shannon-McMillan-Breiman
theorem, which we then use to generalize Kaimanovich's ray approximation and
strip approximation criteria. We give several applications to identify the
Poisson boundary of locally compact groups which act by isometries on
nonpositively curved spaces, as well as on Diestel-Leader graphs and horocylic
products.
