Transfer maps and projection formulas

Transfer maps and projection formulas are undoubtedly one of the key tools in the development and computation of (co)homology theories. In this note we develop an unified treatment of transfer maps and projection formulas in the non-commutative setting of dg categories. As an application, we obtain transfer maps and projection formulas in algebraic K-theory, cyclic homology, topological cyclic homology, and other scheme invariants.