  We define total Frobenius-Schur indicator for each object in a spherical
fusion category $C$ as a certain canonical sum of its higher indicators. The
total indicators are invariants of spherical fusion categories. If $C$ is the
representation category of a semisimple quasi-Hopf algebra $H$, we prove that
the total indicators are non-negative integers which satisfy a certain
divisibility condition. In addition, if $H$ is a Hopf algebra, then all the
total indicators are positive. Consequently, the positivity of total indicators
is a necessary condition for a quasi-Hopf algebra being gauge equivalent to a
Hopf algebra. Certain twisted quantum doubles of finite groups and some
examples of Tambara-Yamagami categories are discussed for the sufficiency of
this positivity condition.
