Title: Finite Chevalley versions of p-compact groups Authors: Carles Broto, Jesper M. Moller Author's e-mail address: broto@mat.uab.es moller@math.ku.dk Address: Carles Broto Departament de Matematiques, Universitat Autonoma de Barcelona, 08193 Bellaterra, Spain Address: Jesper M. Moller Matematisk Institut Universitetsparken 5 DK-2100 Copenhagen Denmark AMS class: 55R35, 55P15, 55P10 Abstract: We describe the spaces of homotopy fixed points of unstable Adams operations acting on p-compact groups and also of unstable Adams operations twisted with a finite order automorphism of the p-compact group. We obtain new exotic p-local finite groups.