An isometrically universal Banach space with a monotone Schauder basis

Abstract: We present an isometric version of the complementably universal Banach space $\mathcal{B}$ with a monotone Schauder basis. The space $\mathcal{B}$ is isomorphic to Pe{\l}czy\'nski's space with a universal basis as well as to Kadec' complementably universal space with the bounded approximation property.