  In this paper, we extend the notion of Shintani descent to general (possibly
disconnected) algebraic groups defined over a finite field $\mathbb{F}_q$. For
this, it is essential to treat all the pure inner $\mathbb{F}_q$-rational forms
of the algebraic group at the same time. We prove that the notion of almost
characters (introduced by T. Shoji using Shintani descent) is well defined for
any neutrally unipotent algebraic group, i.e. an algebraic group whose neutral
connected component is a unipotent group. We also prove that these almost
characters coincide with the "trace of Frobenius" functions associated with
Frobenius-stable character sheaves on neutrally unipotent groups. In the course
of the proof, we also prove that the modular categories that arise from
Boyarchenko-Drinfeld's theory of character sheaves on neutrally unipotent are
in fact positive integral confirming a conjecture due to Drinfeld.
