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Inspired by Stewart Priddy’s cellular model for the \(p\)-local Brown–Peterson spectrum \(\textit{BP}\), we give a construction of a \(p\)-local \(E_\infty \) ring spectrum \(R\) which is a close approximation to \(\textit{BP}\). Indeed we can show that if \(\textit{BP}\) admits an \(E_\infty \) structure then these are weakly equivalent as \(E_\infty \) ring spectra. Our inductive cellular construction makes use of power operations on homotopy groups to define homotopy classes which are then killed by attaching \(E_\infty \) cells.

BP: close encounters of the $$E_\infty $$ E ∞ kind