I've been running a Harn campaign for a while now, and though we've had some hiccups along the way as far as player attendance, we're nearing the conclusion of the campaign. It's been a pretty high-level affair so far, with a lot of planning and maneuvering on a strategic scale. Everyone's having fun, but since we're getting to the end of the game, I've been working on new ideas for another Harn campaign. I want to set the next one in Chybisa, and be more detail-oriented with how the players interact with the world. I plan to have them put in charge of a manor in the Lerenil Barony of Chybisa, and use that as a base of operations as well as a source of adventures. I want to let them get involved in the politics of Kaldor/Melderyn/Chybisa as well as Chybisa's own politics. I want them to get invested in their holdings and in the NPCs they have to deal with on a "daily" basis.

I generally want to keep things grounded in Chybisa, but I also would like to be able to explore some of the things on Lythia (especially "Hadrian's" Wall) in Azeryan. To do that, I need a reason to get them there. Since I've always been fascinated with the crusades, I thought it would be interesting to have the players involved in a major undertaking into Lythia - so they can see what it would be like to leave your home behind for such a long time. The problem is I don't really see much opportunity for there being a "crusade" as we think of it on the Lythian mainland. I understand that I can simply change the canon if I need to, but I'd like to work inside the established world as much as possible. Is there any potential for a major religious conflict on Lythia?

Well, canon is "as of 720 TR". Just proceed one day further and call for an escalating "religious motivated conflict" on mainland Lythia or even an internal temple war over there.
Let some religious instance summon all their faithful warriors for support and your SCs belong to the delegation sent by the Hârnic temples. So, they will have plenty of opportunities to explore Lythia. Perhaps, the initial call was even a fraud to lure them away?

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Ich mag den kleinen blauen Elephanten!

Remember, the motivation for the original crusades was pretty thin. A large part of it was an over supply of heavily armed younger sons + a thin excuse. It seems to me that if you want a crusade, the former is not too an unreasonable assumption, all you need is a trigger. A few possible triggers might be:

Dalkesh and/or Tuvaran tribes invade Byria. "All good Laranians will be forgiven their sins if they fight in the cause of Larani. Everyone knows that Byria consists solely of unmarried women holding wealthy estates... A wife and a mnor for every crusader riding tho their rescue....". The reality may, of course, vary..

Azeryan empire invades eastern Trierzon. Tengela and/or the seat of the Peonian primate fall and must be liberated from the Agrikan hordes... The king of Trierzon will reward all those fighting to free tengela with land and gold. Again, the reality on the ground may vary...

And a slight twist - not a crusade, but might be easier to work in the Shurama (Azeryan's defensive wall). In my p-Harn an important unit of the Azeryan army is the Ivinian Guard - based on the Byzantine Varangian Guard. I include it because it is a potentially fantastic way to get characters to Azeryan and let them get rich seeing the empire (read a biography of Harald Hardrada who served in the Varangian Guard before becoming king of Norway). Historically, the Varangian Guard was heavily Anglo-Saxon in origin, not just Norse/Danish. Hence no reason why the Ivinian guard shouldn't include Harnic knights who, for some reason, need to be out of Harn for a while.

Cheers,
De Coucy

Sounds plausible. Or you could make it an Laranian affair. The Laranians want to improve their standing in the empire of Azeryan. The pontiff promise the emperor a crusade to clear out the Reksyni. In return he wants religious concessions. Surprisingly the Agrikan pontiff agrees. Secretly he make preparations to make sure that the crusade fails.

Or even worse the agrikans save the remnants of the near annhilliated Laranians and chrush the Reksyni.