  Motivated by the higher Chern bands of twisted graphene multilayers, we
consider flat bands with arbitrary Chern number $C$ with ideal quantum
geometry. While $C>1$ bands differ from Landau levels, we show that these bands
host exact fractional Chern insulator (FCI) ground states for short range
interactions. We show how to decompose ideal higher Chern bands into separate
ideal bands with Chern number $1$ that are intertwined through translation and
rotation symmetry. The decomposed bands admit an $SU(C)$ action that combines
real space and momentum space translations. Remarkably, they also allow for
analytic construction of exact many-body ground states, such as generalized
quantum Hall ferromagnets and FCIs, including flavor-singlet Halperin states
and Laughlin ferromagnets in the limit of short-range interactions. In this
limit, the $SU(C)$ action is promoted to a symmetry on the ground state
subspace. While flavor singlet states are translation symmetric, the flavor
ferromagnets correspond to translation broken states and admit charged skyrmion
excitations corresponding to a spatially varying density wave pattern. We
confirm our analytic predictions with numerical simulations of ideal bands of
twisted chiral multilayers of graphene, and discuss consequences for
experimentally accessible systems such as monolayer graphene twisted relative
to a Bernal bilayer.
