In this dissertation we study the K'-theory of a Henselian CM local ring R which is an isolated singularity and has an n-cluster tilting object M. Our main result is a description of the homotopy fiber of the canonical map from K'(End_RM) to K'(R). We also develop a technique for decomposing K₁(End_RM). As we demonstrate, these tools can be used to extract surprisingly explicit information about K'(R) for certain choices of R.