Roe’s algebra is $C^*$-algebra associated to a proper metric space, which reflects its large scale features. The coarse Baum–Connes conjecture provides a framework to compute the K-theory of Roe’s algebra by showing that the coarse assembly map is an isomorphism. In 2015, Chen–Wang–Yu proved the injectivity of the coarse assembly map for spaces that coarsely embed into $l^q$. In this talk, we will address the surjectivity for such $l^q$ coarsely embeddable spaces. Our strategy is to construct a Bott–Dirac operator with an $l^q$ potential on finite dimensional Euclidean space. This approach also leads to an $l^p$-version of the coarse Baum–Connes isomorphism for $l^q$ coarsely embeddable spaces. The talk is based on joint work with Zhizhang Xie, Guoliang Yu, and Bo Zhu.