Bases for cluster algebras from orbifolds

We generalize the construction of the bracelet and bangle bases defined by Musiker, Schiffler and Williams, and the band basis defined by D. Thurston to cluster algebras arising from orbifolds. We prove that the bracelet bases are positive, and the bracelet basis for the affine cluster algebra of type $C_n^{(1)}$ is atomic. We also show that cluster monomial bases of all skew-symmetrizable cluster algebras of finite type are atomic.