  This thesis contains various results on unitary 2-representations of finite
groups and their 2-characters, as well as on pivotal structures for fusion
categories. The motivation is extended topological quantum field theory (TQFT),
where the 2-category of unitary 2-representations of a finite group is thought
of as the `2-category assigned to the point' in the untwisted finite group
model.
  The first result is that the braided monoidal category of transformations of
the identity on the 2-category of unitary 2-representations of a finite group
computes as the category of conjugation equivariant vector bundles over the
group equipped with the fusion tensor product. This result is consistent with
the extended TQFT hypotheses of Baez and Dolan, since it establishes that the
category assigned to the circle can be obtained as the `higher trace of the
identity' of the 2-category assigned to the point.
  The second result is about 2-characters of 2-representations, a concept which
has been introduced independently by Ganter and Kapranov. It is shown that the
2-character of a unitary 2-representation can be made functorial with respect
to morphisms of 2-representations, and that in fact the 2-character is a
unitarily fully faithful functor from the complexified Grothendieck category of
unitary 2-representations to the category of unitary equivariant vector bundles
over the group.
  The final result is about pivotal structures on fusion categories, with a
view towards a conjecture made by Etingof, Nikshych and Ostrik. It is shown
that a pivotal structure on a fusion category cannot exist unless certain
involutions on the hom-sets are plus or minus the identity map, in which case a
pivotal structure is the same thing as a twisted monoidal natural
transformation of the identity functor on the category. Moreover the pivotal
structure can be made spherical if and only if these signs can be removed.
