We investigate the cohomology of a group having finite virtual cohomological dimension in terms of the contributions from finite subgroups. As a result, we prove a variant of Quillen's -isomorphism theorem which remains valid for an arbitrary commutative ring of coefficients and for suitable families of finite subgroups.
"Cohomology of discrete groups and their finite subgroups." J. Math. Soc. Japan 52 (4) 869 - 875, October, 2000. https://doi.org/10.2969/jmsj/05240869