The talk aims to discuss results from an article of W. Smoke from 1987 and some subsequent results. Let A be a Cohen-Maculay local ring and r be an integer. The article studies the Grothendieck group of the category of finitely generated modules of finite projective dimension and codimension at least r, and shows it is generated by perfect cyclic modules of codimension r. For r=0,1,2, one can also replace cyclic modules by complete intersections, but this fails for larger r. The main emphasis will be on an interesting idea of reduction of number of generators to get from arbitrary perfect modules to cyclic perfect modules, which is also used elsewhere, in particular in articles by Dutta, Hochster, etc.
