  In frictionless financial markets, no-arbitrage is a local property in time.
This means that a discrete time model is arbitrage-free if and only if there
does not exist a one-period-arbitrage. With capital gains taxes, this
equivalence fails. For a model with a linear tax and one non-shortable risky
stock, we introduce the concept of robust local no-arbitrage (RLNA) as the
weakest local condition which guarantees dynamic no-arbitrage. Under a sharp
dichotomy condition, we prove (RLNA). Since no-one-period-arbitrage is
necessary for no-arbitrage, the latter is sandwiched between two local
conditions, which allows us to estimate its non-locality.
  Furthermore, we construct a stock price process such that two long positions
in the same stock hedge each other. This puzzling phenomenon that cannot occur
in arbitrage-free frictionless markets (or markets with proportional
transaction costs) is used to show that no-arbitrage alone does not imply the
existence of an equivalent separating measure if the probability space is
infinite.
  Finally, we show that the model with a linear tax on capital gains can be
written as a model with proportional transaction costs by introducing several
fictitious securities.
