  We introduce a generalization of Joyce's motivic Hall algebra by combining it
with Green's parabolic induction product, as well as a non-archimedean variant
of it. In the construction, we follow Dyckerhoff-Kapranov's formalism of
2-Segal objects and their transferred algebra structures. Our main result is
the existence of an integration map under any suitable transfer theory, of
course including the (analytic) equivariant motivic one. This allows us to
study Harder-Narasimhan recursion formulas in new cases.
