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Our main purpose is to describe the category of isotropic cellular spectraover flexible fields. Guided by [6], we show that it is equivalent, as a stable$\infty$-category equipped with a $t$-structure, to the derived category ofleft comodules over the dual of the classical topological Steenrod algebra. Inorder to obtain this result, the category of isotropic cellular modules overthe motivic Brown-Peterson spectrum is also studied, and isotropic Adams andAdams-Novikov spectral sequences are developed. As a consequence, we alsocompute hom sets in the category of isotropic Tate motives between motives ofisotropic cellular spectra.

Cellular objects in isotropic motivic categories