  In this thesis we develop an orbifold theory for a finite, cyclic group $G$
acting on a suitably regular, holomorphic vertex operator algebra $V$. To this
end we describe the fusion algebra of the fixed-point vertex operator
subalgebra $V^G$ and show that $V^G$ has group-like fusion. Then we solve the
extension problem for vertex operator algebras with group-like fusion.
  We use these results to construct five new holomorphic vertex operator
algebras of central charge 24 as lattice orbifolds, contributing to the
classification of the $V_1$-structures of suitably regular, holomorphic vertex
operator algebras of central charge 24.
  As another application we present the BRST construction of ten
Borcherds-Kac-Moody algebras whose denominator identities are completely
reflective automorphic products of singular weight.
