There are several recent constructions by many authors of Eisenstein cocycles of arithmetic groups. I will discuss a point of view on these constructions using equivariant cohomology and differential forms. The resulting objects behave like theta kernels relating the homology of arithmetic groups to algebraic objects. I will also discuss an application to conjectures of Sczech and Colmez on critical values of Hecke L-functions. The talk is based on work-in-progress with Nicolas Bergeron, Pierre Charollois and Akshay Venkatesh.