2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77986We compute the sheaf cohomology of a groupoid built from a local homeomorphism of a locally compact space $X$. In particular, we identify the twists over this groupoid, and its Brauer group. Our calculations refine those made by Kumjian, Muhly, Renault and Williams in the case $X$ is the path space of a graph, and the local homeomorphism is the shift. We also show how the C*-algebra of a twist may be identified with the Cuntz-Pimsner algebra constructed from a certain C*-correspondence.amslatex, 10pp, see also http://unr.edu/homepage/alex/pub/, submitted to JOTOperator Algebras46L55text