  There are a number of (co-)homology theories on coarse spaces. Controlled
operator K-theory is by far the most popular one of them. Our approach is
geometric. We study when does the Roe-algebra of a space restrict to a
subspace. Then we show the Roe-algebra is a cosheaf on the coarse topology. A
result is a Mayer-Vietoris exact sequence in the presence of a coarse cover. We
compute examples as an application.
