  We attempt to generalize the $p$-modular representation theory of finite
groups to finite transporter categories, which are regarded as generalized
groups. We shall carry on our tasks through modules of transporter category
algebras, a type of Gorenstein skew group algebras. The Kan extensions,
upgrading the induction and co-induction, are our main tools to establish
connections between representations of a transporter category and of its
transporter subcategories. Some important constructions and theorems in local
representation theory of finite groups are generalized.
