Long-lived stop at the LHC with or without R-parity

We consider scenarios of gravitino LSP and DM with stop NLSP both within R-parity conserving and R-parity violating supersymmetry (RPC and RPV SUSY, respectively). We discuss cosmological bounds from Big Bang Nucleosynthesis (BBN) and the gravitino abundance and then concentrate on the signals of long-lived stops at the LHC as displaced vertices or metastable particles. Finally we discuss how to distinguish R-parity conserving and R-parity breaking stop decays if they happen within the detector and how to suppress SM backgrounds.