In the seventies of last century, Magnus Landstad characterised the coefficient C*-algebra inside the multiplier algebra of a given crossed product C*-algebra subject to an action of an Abelian locally compact group G. In 2005, Stefaan Vaes extended the Landstad theory for regular locally compact quantum groups. He gave strong indications that this is not possible for non-regular groups. In this talk I shall explain how Landstad-Vaes theory extends for non-regular groups. To this end we have to consider not necessary continuous, but measurable, actions of locally compact quantum groups. For regular locally compact quantum groups any measurable action is continuous, so our theory contains that of Landstad-Vaes. This is a joint work with Stanislaw Lech Woronowicz.

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