Unconditionally saturated Banach space with the scalar-plus-compact property

Abstract: We construct a Bourgain-Delbaen $\mathscr{L}\infty$-space $\mathfrak{X}{Kus}$ with strongly heterogenous structure: any bounded operator on $\mathfrak{X}{Kus}$ is a compact perturbation of a multiple of the identity, whereas the space $\mathfrak{X}{Kus}$ is saturated with unconditional basic sequences.