Let $A,B$ be two unital algebras. We say that $A,B$ are Morita equivalent if there are $A-B$ and $B-A$ bimodules $P,Q$ such that $$P \otimes_{B} Q \cong A, Q \otimes_A P \cong B$$ (as $A-A$ and $B-B$ bimodules).

Suppose that $A,B$ are Morita equivalent. Then one can show that $K$-theory and cyclic and Hochschild cohomologies of them are isomorphic.

How to describe explicitly an isomorphisms $K(A) \cong K(B)$, $HH^{\bullet}(A) \cong HH^{\bullet}(B)$ and $HC^{\bullet}(A) \cong HC^{\bullet}(B)$?