I would like to study the spectral theory of the Dirac Laplacian on a non-compact quotient of the hyperbolic plane by a discrete group (I am particularly interested in the simple case where the surface is a funnel).

Are there any references that are a good start? Thanks a lot for your help!

EDIT: As kindly pointed out in the comment below, the operator referred to above is a first-order operator with coefficients from a Clifford-algebra whose square is the "Laplacian" up to curvature terms.