Delta-invariants for Fano varieties with reductive group actions

In 1987 Tian defined the alpha-invariant for a Fano variety with a reductive group action. He gave a sufficient condition for a Fano variety to admit a Kaehler-Einstein metric in terms of this invariant. Recently Fujita and Odaka suggested the so-called delta-invariant, which characterizes the existence of a KE metric on a Fano variety with finite automorphism group. In my talk I will explain how to define a version of the delta-invariant for a Fano variety with an action of a (possibly infinite) reductive group.