  We explore the origin and Yukawa interactions of the scalars with peculiar
CP-properties which were recently found in a multi-Higgs model based on an
order-4 CP symmetry. We relate the existence of such scalars to the enhanced
freedom of defining CP, even beyond the well-known generalized CP symmetries,
which arises in models with several zero-charge scalar fields. We also show
that despite possessing exotic CP quantum numbers, these scalars do not have to
be inert: they can have CP-conserving Yukawa interactions provided the CP acts
on fermions by also mixing generations. This paper focuses on formal
aspects---exposed in a pedagogical manner---and includes a brief discussion of
possible phenomenological consequences.
