Usually we deploy BPEL business processes on Apache ODE or WSO2 BPS Server included in Tomcat server, can I deploy a business process on Google App Engine's Web Server? Actually I haven't any idea about that!
There is a lot more to running a BPEL process than it seems. You would not deploy the BPEL process, you would deploy Apache ODE to Google App Engine.
Unfortunately, last I checked App Engine has stringent restrictions on the number of threads a program can spawn, making Apache ODE unusable (see 0(their doc)):
The secured "sandbox" environment isolates your application for service and security. It ensures that apps can only perform actions that do not interfere with the performance and scalability of other apps. For instance, an app cannot spawn threads in some ways, write data to the local file system or make arbitrary network connections. An app also cannot use JNI or other native code. The JVM can execute any Java bytecode that operates within the sandbox restrictions.