  A classical result of Bondal-Orlov states that a standard flip in birational
geometry gives rise to a fully faithful functor between derived categories of
coherent sheaves. We complete their embedding into a semiorthogonal
decomposition by describing the complement. As an application, we can lift the
"quadratic Fano correspondence" (due to Galkin-Shinder) in the Grothendieck
ring of varieties between a smooth cubic hypersurface, its Fano variety of
lines, and its Hilbert square, to a semiorthogonal decomposition.
  We also show that the Hilbert square of a cubic hypersurface of dimension at
least 3 is again a Fano variety, so in particular the Fano variety of lines on
a cubic hypersurface is a Fano visitor. The most interesting case is that of a
cubic fourfold, where this exhibits the first higher-dimensional hyperk\"ahler
variety as a Fano visitor.
