Morava -theory of filtered colimits

Morava -theory is a much-studied theory in algebraic topology, but it is not a homology theory in the usual sense, because it fails to preserve coproducts (resp. filtered homotopy colimits). The object of this paper is to construct a spectral sequence to compute the Morava -theory of a coproduct (resp. filtered homotopy colimit). The -term of this spectral sequence involves the derived functors of direct sum (resp. filtered colimit) in an appropriate abelian category. We show that there are at most (resp. ) of these derived functors. When , we recover the known result that homotopy commutes with an appropriate version of direct sum in the -local stable homotopy category.