  We introduce a new method for expanding an abelian category and study it
using recollements. In particular, we give a criterion for the existence of
cotilting objects. We show, using techniques from noncommutative algebraic
geometry, that our construction encompasses the category of coherent sheaves on
Geigle-Lenzing weighted projective lines. We apply our construction to some
concrete examples and obtain new weighted projective varieties and analyse the
endomorphism algebras of their tilting bundles.
