On the spectrum bo∧tmf

M. Mahowald, in his work on bo-resolutions, constructed a bo-module splitting of the spectrum bo∧bo into a wedge of summands related to integral Brown–Gitler spectra. In this paper, a similar splitting of bo∧tmf is constructed. This splitting is then used to understand the bo∗-algebra structure of bo∗tmf and allows for a description of bo∗tmf.