Lin, Hauxin2010-06-012010-06-0119922010-06-01http://hdl.handle.net/1828/2827We give an answer to the question when the unitary group of the corona algebra of a simple AF-algebra is connected. We also compute the K-groups of the multiplier algebras and corona algebras of certain simple C*-algebras. For example, if A_\theta is an irrational rotation C*-algebra and A is a non-stable hereditary C*-subalgebra of A_\theta \varotimes K, then we find that K_1(M(A)) = K_1(M(A)/A) = {0} and K_0(M(A)) = R.enTechnical Report