Given a regular C*-algebraic locally compact quantum group (S_r,Δ) with universal quantum group (S_f,Δ_f), a C*-algebra A, and a sufficiently well-behaved full coaction, we construct natural lattice isomorphisms from the strongly coaction invariant ideals of A to the strongly coaction invariant ideals of full and reduced crossed product C*-algebras as an application of the "ladder technique" developed by the author, S. Kaliszewski, John Quigg and Dana P. Williams. In particular, these lattice isomorphisms are determined by either the maximality or normality of the coaction. This result directly generalizes a recent theorem proven by the aforementioned authors for locally compact groups, which in turn generalized a theorem of Elliot Gootman and Aldo Lazar for amenable groups.

I would like to give my sincere thanks to Stefaan Vaes, Alcides Buss and Siegfried Echterhoff for their remarkable patience and many helpful conversations assisting me in learning the basics of this theory.