For a homology theory \(E_*(-)\) an \(E\)-detecting category for a space \(X\) is a subcategory \(C\) of the homotopy category, closed under finite products such that there is an isomorphism \(J:\text{colim} E_*(Z)\to E_*X\) where \(C_X\) is the category with \(C_X\) objects the homotopy classes of maps \(Z\to X\) \((Z\in C)\) and obvious morphisms. The aim of this paper is to study the set \(H\) Ring \((\Omega^\infty G,\Omega^\infty E)\) for the case when the category of finite products of \(\mathbb{C} P^\infty\) is a detecting category for \(\Omega^\infty G\). Here \(\Omega^\infty G\) denotes an infinite loop space which is a ring up to homotopy such that for any space \(X\) there is an isomorphism \(G^0(X)\cong [X,\Omega^\infty G]\) and \(G^*(-)\) a multiplicative cohomology theory. For the two periodic case under suitable conditions there is a bijection \(H\) Ring \((\Omega^\infty G,\Omega^\infty E)\leftrightarrow FG(G^{* \leq 0},F_G)\) where \(FG\) denotes some quotient of the formal group law category. In the nonperiodic case, a similar result is proved with a more complicated category \(VFG\) in place of \(FG\).