1) General Call by DAAD for Proposals
You can find an overview about general calls for proposals from the DAAD regarding international exchange including the respective target group and procedures here.
2) Exchange with North America
The State of Land Baden-Württemberg supports an exchange program with specific regions in Canada and the US, also covering Research Stays. The focus is on initiating and maintaining networks between participating institutions. Travel costs are covered to a fixed amount (usually 1200-1400 EUR), other funds and the duration of stay depend on the specific program. The exchange for scientists is possible with universities in the States of Ontario/Canada, Connecticut/USA, North Carolina/USA and Oregon/USA as well as with the University of Massachusetts/USA. You find in-depth information by using the respective links.
3) Find Cooperations with Partners in "Global South"
DAAD funds initiatives to establish/support cooperations with universities and institutes ind developing countries on departmental level. These initiatives aim at establishing long-term cooperations with the goal to improve respective structurs of the foreign partner. fördert Initiativen zur Kooperationsfindung/Vertiefung von Kooperationen mit Universitäten/Instituten in Entwicklungs/Schwellenländern auf Fachbereichsebene. Initiativen sollen zu einer langfristigen Kooperation zwischen den Partnern führen mit dem Ziel, Strukturen der ausländischen Partner-Institutionen zu verbessern. Funding amount is between 15,000 und 20,000 EUR. Find more information here.