Let $A$ be a separable unital quasidiagonal $C^\*$-algebra.
What can be said about the $K$-theory of $A$, for example some properties? Especially, are there some criterions to decide whether or not $K\_\*(A)$ has torsion?
I appreciate any reference request in this direction. Thank you.



K-group properties of quasi-diagonal $C^*$-algebras
This is not necessarily an answer, but it was too long for a comment:


Note that for any separable unital $C^\*$-algebra $A$ its suspension $SA := C\_0(\mathbb{R}) \otimes A$ is quasidiagonal. This can be found as Corollary 7.3.7 in the (excellent) book "$C^\*$-algebras and Finite-dimensional Approximations" by Brown and Ozawa. Here is the [link](https://books.google.co.uk/books?id=kQMPCgAAQBAJ&pg=PA237&lpg=PA237&dq=suspension%20quasidiagonal%20C*%20algebra&source=bl&ots=B6AIHW2KZl&sig=3efbj6y1iYHNnY0cq8d2tp66gaI&hl=en&sa=X&ved=0ahUKEwikmtv796vUAhWqKsAKHYJXD10Q6AEIKjAB#v=onepage&q=suspension%20quasidiagonal%20C*%20algebra&f=false). 


Using $K\_i(SA) \cong K\_{i+1}(A)$ and Bott periodicity it follows that quasidiagonality does not impose any restrictions on the K-theory groups, if you allow *non-unital* $C^\*$-algebras (like $SA$). 


