. . . I was thinking about the receiver that is using bitcoin-qt wallet . . .
. . . the full wallet is usually perceived as a better solution than any light wallet, in terms of security . . .
In terms of Bitcoin-Qt wallet, this attack would be VERY expensive. The attacker would need to have control of nearly as much bitcoin block hashing power as the rest of the world combined if they wanted to provide blocks at a reasonable rate of about one every 10 minutes. They *might* be able to get away with about one-sixth of the world's hash power if they knew for sure that their vicitim was only going to wait for 1 confirmation but...
1) The average time for the attacker to create a valid forked block will be an hour (some blocks will take even longer).
2) One sixth of the world's hashpower is still very expensive.
3) The more value you are exchanging, the more confirmations you should wait for, and the more suspicious you should be of unusual circumstances
4) It is going to take nearly an hour to get that 1 confirmation which is a lot of time for the victim to become suspicious and decide to check on things.
5) All that hashpower could have earned real bitcoins by mining on the real blockchain (approximately 12.5 bitcoins per hour). So, unless the attack is for more than 12.5 bitcoins or is driven by pure vengeance (And not a profit motive), the attacker probably could have earned a lot more money by simply mining instead of attacking.
6) If the attack IS for more than 12.5 BTC... See #3
. . . So should the attacker be certain his victim only uses a lite wallet he can invite his victim to his home to receive the payment? . . .
You are changing the rules here. You said that you were thinking about Bitcoin-Qt BECAUSE it is usually perceived as a better solution than any light wallet. Now you are saying that the victim is going to use a worse solution?
If the user is willing to use any system the requires some amount of trust (Lite wallet, hosted wallet, blockchain explorer, paypal, credit card, paper check from a bank account, etc), then it will always be possible to take advantage of that trust with enough effort. The more trust that is needed the easier it will be to take advantage of that trust.
And would it be possible for the attacker to fake the hashpower? As he has all the nodes he can modify the bitcoind in order to drop the difficulty and to mine with a CPU, but to communicate to "blockchain" the hashpower multiplied by let say 10whatever?
No. Bitcoin-Qt doesn't care how much hash power you have. It just cares if you were able to provide a valid hash. On average it requires a LOT of attempts before you stumble across a valid hash. If you don't actually have enough hash power, then it is going to take you a very long time to try enough attempts to stumble across a valid hash. At the current difficulty, it requires generating (on average) approximately 46,800,000,000,000,000,000,000 hashes before stumbling on a valid hash. Without a lot of hashpower, it is going to take a long time to generate that many hashes.
It isn't going to be enough to "modify the bitcoind". The attacker doesn't get to choose the valid difficulty. The victim's Bitcoin-Qt calculates the difficulty itself (it does not trust the difficulty that it hears from other nodes). It does this by looking at the amount of time it took to calculate the previous 2,016 blocks (approximately 2 weeks of blocks), and the difficulty that those blocks were calculated at. The attacker would need to modify the victim's Bitcoin-Qt if he wanted to change the difficulty value that the victim's software would accept.
There is no hashpower "communicated to the blockchain". There is only a hash that is either valid (below the current difficulty threshold) or isn't valid (is above the current difficulty threshold). Since the victim's Bitcoin-Qt gets to set that difficulty threshold itself, either the attacker generated enough hashes to stumble across blocks with a low enough hash, or they didn't generate enough and haven't yet found blocks with a low enough hash.
And another thought. What if the attacker performs the same attack without inviting his victim to a physical place, just by knowing the victims IP and isolating from him the right net and offering only connections to the fake nodes?
Place has nothing to do with the attack you are trying to describe. The point of your described attack is simply that the victim is isolated from other Bitcoin nodes and is forced to communicate with nodes that the attack controls. There may be MANY different ways to accomplish this, but in the end it isn't likely to be a profitable attack unless you have a VERY VERY gullible victim.