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We consider the homology theory of \'etale groupoids introduced by Crainicand Moerdijk, with particular interest to groupoids arising from topologicaldynamical systems. We prove a K\"unneth formula for products of groupoids and aPoincar\'e-duality type result for groupoids which are principal with orbitshomeomorphic to a Euclidean space. We conclude with a few example computationsfor systems associated to nilpotent groups such as self-similar actions, and wegeneralize previous homological calculations by Burke and Putnam for systemswhich are analogues of solenoids arising from algebraic numbers. For the lattersystems, we prove the HK conjecture, even when the resulting groupoid is notample.

Homology and K-theory of dynamical systems. IV. Further structural results on groupoid homology