On a Spectrum-level Splitting of the $BP⟨2⟩$-Cooperations Algebra

In the 1980s, Mahowald and Kane used Brown-Gitler spectra to construct splittings of $bo\wedge bo$ and $BP⟨1⟩\wedge BP⟨1⟩$. These splittings helped make it feasible to do computations using the $bo$- and $BP⟨1⟩$-based Adams spectral sequences. In this paper, we construct an analogous splitting for $BP⟨2⟩\wedge BP⟨2⟩$.