A Thom Spectrum Model for $C_2$-Integral Brown--Gitler Spectra

A Thom spectrum model for a $C_2$-equivariant analogue of integral Brown--Gitler spectra is established and shown to have a multiplicative property. The $C_2$-equivariant spectra constructed enjoy properties analogous to classical nonequivariant integral Brown--Gitler spectra and thus may prove useful for producing $C_2$-equivariant analogues of splittings of $BP \langle 1 \rangle \wedge BP \langle 1 \rangle$ and $bo \wedge bo.$

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