  We define and calculate inner products of 2-representations. Along the way,
we prove that the categorical trace Tr(-) of [Ganter and Kapranov,
Representation and character theory in 2-categories, Sec. 3] is multiplicative
with respect to various notions of categorical tensor product, and we identify
the center of the category V^G of [loc. cit., Sec. 4.2]. We discuss
applications, ranging from Schur's result about the number of projective
representations to a formula for the Hochschild cohomology of a global quotient
orbifold.
