Synthetic equivariant spectra and complex bordism

I’ll discuss and motivate a theory of synthetic equivariant spectra in which equivariant stable homotopy types are suitably resolved by  even-dimensional cells. This recovers the Adams—Novikov spectral sequence based on equivariant complex bordism and additionally admits an interpretation in terms of motivic homotopy theory over the complex numbers. If time permits, I’ll discuss  how these equivariant statements (at abelian compact Lie groups) are quite natural extensions of the corresponding nonequivariant statements that reflect the structure of a globally equivariant “decompletion" of the standard Quillen formal group on algebraic cobordism.