  We present a rich source of Hopf algebras starting from a cofinite central
extension of a Noetherian Hopf algebra and a subgroup of the algebraic group of
characters of the central Hopf subalgebra. The construction is transparent from
a Tannakian perspective. We determine when the new Hopf algebras are
co-Frobenius, or cosemisimple, or Noetherian, or regular, or have finite
Gelfand-Kirillov dimension.
