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A Thom spectrum model for a $C_2$-equivariant analogue of integralBrown--Gitler spectra is established and shown to have a multiplicativeproperty. The $C_2$-equivariant spectra constructed enjoy properties analogousto classical nonequivariant integral Brown--Gitler spectra and thus may proveuseful for producing splittings of $BP \langle 1 \rangle \wedge BP \langle 1\rangle$ and $bo \wedge bo$ in the $C_2$-equivariant setting.

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