Trading as in trading single-stocks? Most (all?) Norwegian equity brokers/banks offer access to local and international markets and transaction fees are quite low - but as it is generally a fixed-sum-minium they can take a chunk out of very small trades. For index funds the going rate is management fees of around 0.20% - regardless if local, regional or global. Buying and selling index funds is generally free. There are ETFs on the local market and you can prob buy any listed ETF worldwide quite easily.
He should first read up on Aksjesparekonto (AKS) (deferred tax-account for holding equities and/or mutual funds) and probably also IPS (individual retirement savings with delayed tax).
A very central point is that the AKS only offers deferred tax for EU/EEC equities. You can however buy say an index fund investing only in the US market and put it in there, but you can't do US ETFs for example. As of this year there is also deferred tax on dividends. You cannot put bonds or bond funds in there. Anything you put in (aka purchase price) you can take out tax-free at any time, you only incur tax (or tax deductions) for profit (or loss). By law cash sitting in the account earns 0% interest.