SUBGROUP POSETS, BREDON COHOMOLOGY AND EQUIVARIANT EULER CHARACTERISTICS

For discrete groups G with a bound on the order of their finite subgroups, we construct Bredon projective resolutions of the trivial module in terms of projective covers of the chain complex associated to the poset of finite subgroups. We use this to give new results on dimensions of (E) under bar Gamma and to reprove that for virtually solvable groups, (cd) under bar Gamma = vcd Gamma. We also deduce a formula to compute the equivariant Euler class of (E) under bar Gamma for Gamma virtually solvable of type FP infinity and use it to compute orbifold Euler characteristics.