Index theory for H-elliptic and transversally H-elliptic operators from KK-theoretic viewpoint

This paper provides a comprehensive definition for transversally H-elliptic operators and explores the index theorem of H-elliptic and transversally H-elliptic operators through the lens of KK-theory, employing Kasparov's approach. Furthermore, our analysis incorporates a detailed examination of conditions, specifically delving into the Fourier transform of the nilpotent group C^-algebra.