Chromatic homotopy theory uses the algebraic geometry of smooth 1-parameter formal groups to separate stable homotopy theory into periodic layers. The 1st layer recovers the image of Adams’ J homomorphism and the real Bott periodicity of the real topological K-theory KO. In this talk, I will present a generalization of the real Bott periodicity of KO to general layers at prime 2. The proof takes inspiration from the breakthroughs of Hill—Hopkins—Ravenel’s solution to Kervaire invariant one problem. This is based on joint works with Zhipeng Duan, XiaoLin Danny Shi, Guozhen Wang, and Zhouli Xu.