  We study a family of subrings, indexed by the natural numbers, of the mod-p
cohomology of a finite group G. These subrings are based on a family of
v_n-periodic complex oriented cohomology theories and are constructed as rings
of generalised characteristic classes. We identify the varieties associated to
these subrings in terms of colimits over categories of elementary abelian
subgroups of G, naturally interpolating between the work of Quillen on
var(H^*(BG)), the variety of the whole cohomology ring, and that of Green and
Leary on the variety of the Chern subring, var(Ch(G)). Our subrings give rise
to a "chromatic" (co)filtration, which has both topological and algebraic
definitions, of var(H^*(BG)) whose final quotient is the variety var(Ch(G)).
