The e-shop embed an (additional) payment button and a script on the checkout form, just like with Stripe or Paypal. When the user clicks the button it will create a payment on my server with the relevant data from the e-shop, like bank account number, amount, currency, and open a new browser window on my site with the above payment information. This looks like this: http://i.imgur.com/m1ltZNg.png
To complete the payment the user must install the Chrome extension and navigate to own your online bank, make the transfer to the e-shop's bank account using the information given above. This is likely free. When the transfer have been made the user must export the transfer (or recent account transactions) to .CSV format, which many banks offer. The Chrome extension will intercept this, verify the payment to the e-shop on my server and finally callback to the e-shop's checkout form.
Could it work?
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Thoughts:
Planning for launch in Germany (and EU) which has standardized CAMT formatting for data exports.
There should be some mechanism to verify that this works with a given online bank.