A Thom spectrum model for 𝐶₂-integral Brown–Gitler spectra

A Thom spectrum model for a C 2 C_2 -equivariant analogue of integral Brown–Gitler spectra is established and shown to have a multiplicative property. The C 2 C_2 -equivariant spectra constructed enjoy properties analogous to classical nonequivariant integral Brown–Gitler spectra and thus may prove useful for producing C 2 C_2 -equivariant analogues of splittings of B P ⟨ 1 ⟩ ∧ B P ⟨ 1 ⟩ BP 1 BP 1 and b o ∧ b o bo bo .