  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.
