Аннотация:DOI.org/10.1007/978-3-030-37326-9_16Abstract. This article is based on the author’s talk at the international conference dedicated to the memory of Professor B. Yu. Sternin (Moscow, November6–9, 2018). The Hochschild homology and cohomology of a group algebra canbe described via the homology and cohomology of the classifying space of theadjoint action groupoid of the group under a suitable assumption on the finite-ness of support of the cohomology groups. The difference between homologyand cohomology leads to a correction to results in D. J. Benson’s book Representations and cohomology (vols. I–II, Cambridge Univ. Press, Cambridge,1991