for any $c_2$-equivariant spectrum, we can functorially assign two non-equivariant spectra - the underlying spectrum and the geometric fixed point spectrum. they both induce maps from $ro(c_2)$-graded cohomology to classical cohomology. in this talk, i will compare the $ro(c_2)$-graded squaring operations with the classical squaring operations along the induced maps. this is joint work with prasit bhattacharya and bertrand guillou.