  In this work, we introduce a class of Timmermann's measured multiplier Hopf
*-algebroids called algebraic quantum transformation groupoids of compact type.
Each object in this class admits a Pontrjagin-like dual called an algebraic
quantum transformation groupoid of discrete type. This compact/discrete duality
in the framework of algebraic quantum transformation groupoids recover the one
between compact and discrete Van Daele's algebraic quantum groups. Among the
non-trivial examples of algebraic quantum transformation groupoids of compact
type, we give constructions arising from Fell bundles and quantum quotient
spaces.
