There are various definitions of boundary of a hyperbolic group. Which of those generalize to semi-hyperbolic groups (in the sense of Alonso and Bridson)?
The example I have in mind is a semisimple group over a nonArchemedian local field.The answer I'd like to get is something like a nonHausdorff space which is a union of partial flag manifolds $G/P$ (which can be described as the quotient of the complement to $G$ in the De Concini-Procesi compactification by the right action of $G$).