Bredon cohomological dimension for virtually abelian stabilisers for CAT(0) groups.

Given a discrete group G , for any integer r ≥ 0 we consider the family of all virtually abelian subgroups of G of rank at most r. We give an upper bound for the Bredon cohomological dimension of G for this family for a certain class of groups acting on CAT (0) spaces. This covers the case of Coxeter groups, Right-angled Artin groups, fundamental groups of special cube complexes and graph products of finite groups. Our construction partially answers a question of Lafont. [ABSTRACT FROM AUTHOR]