In the 1980s, Mahowald and Kane used Brown-Gitler spectra to construct splittings of $bo ⋀ bo$ and $l ⋀ l$. These splittings helped make it feasible to do computations using the $bo$- and $l$-based Adams spectral sequences. In this talk, we will construct an analogous splitting for $BP<2> ⋀ BP<2>$ at primes $p \ge 5$.
