While various versions of Chern character are maps from K-theory to some (co)homology of a space, algebra, scheme, the Dennis trace map underlies this phenomenon at the more fundamental level of K-theory space.
It has a refinement to spectra by the cyclotomic trace.
Ib Madsen, Algebraic K-theory and traces, Current Developments in Mathematics, 1995.
John Rognes, after Marcel Bökstedt, Trace maps from the algebraic K-theory of the integers, K-theory archive
M. R. Kantorovitz, Adams operations and the Dennis trace map, JPAA 144, 1 (Dec 1999), 21-27 [doi]
M. R. Kantorovitz, C. Miller, An explicit description of the Dennis trace map, claudia-revised.ps