Challah, Chapter 3, Mishnah 6:
The Mishnah deals with a convert who converted while he already had dough in his possession, and with the question of which moment determines the obligation of challah: the time when he was still a non-Jew, or after he converted.
"Ger shenisgayer... na'aseis ad shelo nisgayer - patur" - "na'aseis" means that the dough was rolled together. If it was rolled before he converted, it is exempt from challah, since at that moment he was not yet Jewish, and a non-Jew is not obligated in challah. The obligation of challah takes effect at the moment the dough is rolled, and that took place at a time when he was not Jewish.
"Umishenisgayer - chayav" - if the dough was rolled after the conversion, he is obligated in challah.
"Ve'im safek - chayav" - because of the doubt, the obligation of challah rests upon him. Such a doubt can arise when the dough is his and he has already undergone conversion, but someone else prepared it for him, and it is not known at what point in the day it was made, before the conversion or after it.
"Ve'ein chayavin aleha chomesh":
There is something unique about this challah that is taken because of a doubt: even though he is required to separate it, one is not liable for a chomesh on it. That is, if a non-kohen ate it, he is not liable for the additional fifth. Normally, a non-kohen who eats Terumah pays the principal and a chomesh - he returns the principal and adds a fifth to it, which is a quarter of the principal, as a fine; but in this case he is not required to add it.
The commentators discussed why this is so, and two approaches were offered:
Some say that only the principal is required, because its law is like that of theft: he must return the money to the tribe of kohanim, to at least one kohen, and this restitution is obligatory, but the fine is not included.
And others explain that the payment of the principal is in the nature of atonement - returning the Terumah or the challah atones - and this atonement applies to the principal, to the main obligation, and not to the chomesh. And some raised a difficulty with this, that the chomesh too should be part of the atonement.
The view of Rabbi Akiva:
Up to this point we have taken the position in the Mishnah that the determining time, both for the question of when a person is considered Jewish and for the question of when the obligation of challah takes effect, is the moment the dough is made and rolled together. Rabbi Akiva disagrees and says: "Hakol holech achar hakerimah batanur".
That is, determining the time at which the obligation of challah takes effect depends on the bread forming a crust in the oven - the moment the crust forms, from which point on the dough is considered baked. Accordingly, if he was Jewish before that point, he is obligated in challah, and if he was not Jewish, he is exempt. This is the criterion according to Rabbi Akiva.