New variables related to spin-structures are introduced with the aim of replacing the metric in the description of gravity. These new variables provide a general framework which allows one to deal with interactions between spinors and a dynamical gravitational field, thus generalizing the notion of spinors on curved spaces. In this framework there is no action of space-time diffeomorphisms on the configuration bundle, but there is covariance with respect to automorphisms of a suitable principal bundle, as it is standard in gauge theories. A concrete example of spinors interacting with gravity is considered as an application.

PACS numbers: 04.20.Fy, 04.20.Gz