[Exim] Newbie SMTP/ISP-Problem ...

Hello Exim-Users,

maybe I'm missing the point but I can't find anything in the FAQ or
elsewhere concerning my problem.

I'd like to use my own Linux-Box as SMTP-host because my ISP always
rewrites my e-mail adress
but I'd like to use my standard alias. (i use email@??? but after
sending via my ISP the recipient
would see email@??? and would answer to it ... ) The problem ist,
that certain other ISPs will not
accept emails sent from dial-up hosts (in this case, my privat pc), so
how can I fix this???

Thank you for help,

Roland Heiber