### Traces in oriented homology theories of algebraic varieties, by Konstantin I. Pimenov

The present preprint is the first one in a short series of preprints.
The main aim of this series is to give a proof of "the only
non-trivial result on algebraic cobordism" stated by V. Voevodsky in
his preprint on Milnor Conjecture. In this preprint we introduce the
notion of oriented homology theory on smooth algebraic varieties
following the strategy suggested by Panin. We consider three
structures on a homology theory: an orientation, a Thom structure and
a Chern structure. We describe relations of these structures to each
other. These should be considered as a preliminary to construct trace
structure on an oriented homology theory. The proper construction of
the trace structure is postponed to the next preprint.

Konstantin I. Pimenov <kip302002@yahoo.com>