Morava $E$-theory of filtered colimits

Morava $E$-theory $E_{n*}^{\vee }(-)$ 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 $E$-theory of a coproduct (resp. filtered homotopy colimit). The $E_{2}$-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 $n-1$ (resp. $n$) of these derived functors. When $n=1$, we recover the known result that homotopy commutes with an appropriate version of direct sum in the $K(1)$-local stable homotopy category.