  We construct a family of orthogonal characters of an algebra group which
decompose the supercharacters defined by Diaconis and Isaacs. Like
supercharacters, these characters are given by nonnegative integer linear
combinations of Kirillov functions and are induced from linear supercharacters
of certain algebra subgroups. We derive a formula for these characters and give
a condition for their irreducibility; generalizing a theorem of Otto, we also
show that each such character has the same number of Kirillov functions and
irreducible characters as constituents. In proving these results, we observe as
an application how a recent computation by Evseev implies that every
irreducible character of the unitriangular group $\UT_n(q)$ of unipotent
$n\times n$ upper triangular matrices over a finite field with $q$ elements is
a Kirillov function if and only if $n\leq 12$. As a further application, we
discuss some more general conditions showing that Kirillov functions are
characters, and describe some results related to counting the irreducible
constituents of supercharacters.
