Charmenability of arithmetic groups of product type

We discuss special properties of the spaces characters and positive definite functions, as well their associated dynamics, for arithmetic groups product type. Axiomatizing these properties, we define notions charmenability charfiniteness study applications to topological ergodic theory unitary representation given groups. To do that, singularity equivariant normal ucp maps between certain von Neumann algebras. apply our discussion also acting on trees.